SPARTANBURG, S.C.—You could see why Ted Cruz might be getting a little frustrated. So many of the voters that rightfully belonged to him were, lately, stubbornly choosing to back other candidates instead.

Donald Trump. Marco Rubio. Even—would you believe it?—Jeb Bush. Couldn’t they see they were getting it wrong? Sitting in a shiny leather armchair on the stage of a megachurch here on Wednesday, Cruz reflected on the previous Saturday’s vicious dogfight of a Republican debate, which had featured a level of personal invective between the candidates that was unusual even for a hotly contested primary.

“It was more than a little striking, on Saturday night, to see more than one of the candidates on the stage, when you brought up their record, they just turned and began yelling, ‘Liar, liar, liar!’” Cruz said, adding piously, “That is not the way political discourse should be engaged in.” This was the same Ted Cruz who had, a few hours before, held a press conference to theatrically dare Donald Trump to sue him for a commercial in which Cruz’s campaign asserted, “We cannot trust Donald Trump.” Trump’s lawyers had asked him to take it down.

Saturday’s South Carolina primary poses a crucial test for Cruz, who had hoped his win a couple weeks ago in the Iowa caucuses would give him momentum in the Southern states that are similarly loaded with conservative and religious voters. But rather than gaining ground, Cruz’s standing in recent South Carolina polls—which are hard to trust, as they are all over the place—has been static or even declining; all of them show Trump ahead by double digits, and some put Cruz in danger of losing his second-place standing. If he can’t do well here, his strategy going forward, which focuses on the other deep-South states that vote next month, will be thrown into doubt.

But the way the Republican campaign is going in South Carolina is raising an even bigger question, not just for Cruz but for the party as a whole: Can anybody win this thing?

Welcome to the great Republican stalemate. No candidate commands anything approaching a majority of the primary electorate. Trump, in first place, pulls about one-third of the vote. All the candidates are locked in their narrow, mutually exclusive “lanes” of different kinds of voters. And rather than back down or seek accommodation, they keep upping the ante.

The paralyzed state of the field has even raised the possibility that no candidate will have a majority of delegates when the Republican convention opens in Cleveland in July, forcing a second ballot and a chaotic fight on the convention floor. The idea of a contested convention, perennially batted about but usually a rules-nerd’s pipe dream, seems a distinct possibility this time around.

The primary, in other words, is just as gridlocked as Washington, where bills can’t get passed and the Supreme Court can’t make decisions. A majority of Republican voters value standing on principle more than compromise; they see gridlock as the only bulwark against tyranny, and refusing to back down as the mark of character. Now that attitude has come to the political campaign, with six remaining candidates who swear they will never yield, and a party so divided its factions may be fundamentally irreconcilable.

But back to Saturday’s debate, in which Trump was booed for saying George W. Bush knowingly lied about weapons of mass destruction in Iraq; Marco Rubio said Cruz had a “disturbing pattern” of “just … telling lies”; Trump called Jeb Bush weak and a liar and Cruz “the single biggest liar” and “a nasty guy”; and Bush said Trump was the weak one, and disinvited him from an upcoming rally with the former president. Trump shot back, “I don’t want to go.”

Midway through the debate, the GOP message maven Frank Luntz tweeted, “Seriously, this is insane. The GOP is destroying itself tonight, and they have no one to blame but themselves.” On Thursday, I ran into Luntz in the press area of a Rubio town hall in Anderson. He looked depressed. He’d seen tough elections before, he said, but this one was “poisonous,” and would send independent voters fleeing to the comparatively civil Democrats.

As Luntz spoke, Rubio’s campaign was straining mightily to gin up controversy over the Cruz campaign’s creation of a website attacking Rubio for his position on trade—a position Cruz had once shared. The site featured a stock photograph that had been altered so that it seemed to show Rubio and Obama shaking hands. Rubio’s adviser, Todd Harris, was passing out paper copies of the photo and seething that it was a “deception” that proved Cruz was “desperate.”

Despite the conventional wisdom that Cruz is an “outsider” candidate and Rubio an “establishment” one, Rubio’s campaign has long believed Cruz’s voters are susceptible to being peeled off. Rubio representatives can frequently be found outside Cruz events, handing out fliers accusing Cruz of supporting “European style taxes” or plastic pocket calculators labeled “Ted Cruz: Political Calculator,” accompanied by a sheet detailing Cruz’s alleged reversals.

Rubio, taking questions from reporters in Anderson, was accompanied by the state’s popular governor, Nikki Haley, who had just endorsed him. She waved off suggestions that things had gotten unbecomingly ugly. “When you come to South Carolina, politics is a blood sport,” she said. “I wear heels—it’s not a fashion statement, it’s because you’ve got to be prepared to kick at any time.”

Rubio was eager to talk about Cruz, who was, he said, “just making things up!” But the press had something even more outrageous on its collective mind: Trump had managed to get into a war of words with the Pope. It is 2016, and there are no limits on the fight in the GOP.

Not long after Rubio spoke, half an hour up the road in Clemson, John Kasich’s strategist, John Weaver, undertook to explain to me why all of the other candidates could not possibly win.

We had just watched Kasich, the rough-hewn Ohio governor who pulled off a surprise second-place showing in last week's New Hampshire primary, make a plea for unity and compassion to a packed auditorium. He insisted that there was a “Kasich lane” of the electorate in addition to the establishment and anti-establishment categories; he urged kids to stay off drugs; he gave a hug to a student going through a hard time.

As we stood in the brisk sunshine outside the Strom Thurmond Institute, Weaver, who has the dour sarcasm of the political lifer, laid it out. Cruz, he said, was not well-liked enough to win the hearts of the mainstream of the GOP electorate. “His negative [ratings] are 50 and climbing,” Weaver said. “It’s like he’s trying to outdo Beelzebub.”

As for Rubio, Weaver wanted to know how he planned to parlay third place in Iowa, fifth place in New Hampshire, and a potential third-place showing in South Carolina into eventually winning it all. (National Review on Thursday echoed this idea: “If Rubio can’t win here, with most of the state’s Republican apparatus supporting him, where can he?”) “He’s a rare political talent, like John Edwards, but he’s not built for the long haul,” Weaver said.

Bush, he said, was “so done. He’ll be out of this race by next week, and if he’s not, he’ll be like an athlete who stayed one season too long.” He noted that Bush’s super PAC was currently spending half its television budget in South Carolina attacking Kasich, and he pointed to a report, hotly denied by the Bush team, that the campaign was out of money. Ben Carson, he opined, was “a lovely man, but his campaign’s going nowhere.”

What about Trump, I wanted to know—you know, the frontrunner? Weaver insisted that Trump’s support was solid but had reached its upper limit, and that a majority of Republican voters would refuse to support him in the end. “Trump has a really hard floor, and his conduct in recent days has toughened it, but he also has an equally hard ceiling,” Weaver said, predicting that Trump’s one-third of the vote wouldn’t look so mighty when there were few enough other candidates that they could command a similar share.

That leaves Kasich, of course, but Weaver’s affirmative case for his candidate seemed as farfetched as the candidates he derided. Kasich hoped to collect some delegates in the Super Tuesday states of Vermont, Massachusetts, Virginia, and Tennessee, all of which award delegates proportionally to the voting results rather than giving them all to the winner. His was “the best organized campaign in Mississippi,” and would “punch above our weight” there on March 8, when he also expected to do well in Michigan. And on March 15—nearly a month away—would come his home state of Ohio.

At no point, I noticed, did Weaver actually forecast a win for his candidate; it was a strategy to rack up delegates and hope that the field will clear—and that he wouldn’t get lost in the shuffle. I asked him what he would consider a good showing in South Carolina, where Kasich had decided to campaign vigorously in the final days despite a skin-and-bones campaign operation here and a struggle to connect with the state’s conservative voters.

“We want to do well enough to keep Jeb from doing well,” Weaver said bluntly. “If we knock him out of the race, it’s a victory.”

The problem with this campaign is that nobody seems inclined to heed the writing on the wall. In an interview with NBC on Tuesday, Jeb insisted he was “in it for the long haul.” His campaign’s strategy is similar to Kasich’s—to stick around and wait out the other non-Trump candidates. Carson, meanwhile, said on Thursday that he still liked his chances and that it was too soon to count him out: “You don’t call the game after the second or third inning.”

All these men are carrying grudges that losing might only inflame. Bush has an Oedipal relationship with Rubio, a onetime protégé he has turned on in sharply personal terms, tearing apart the Florida Republican establishment that felt loyal to both men. Carson may be staying in to get back at Cruz, whom he accuses of dirty tricks in Iowa, and who would almost certainly get most of his voters if he dropped out. Kasich still harbors some resentment of the Bushes from his first presidential run, in 2000: George W. Bush coopted his message of compassionate conservatism, steamrolled the GOP establishment, and killed the White House dreams of the brash young representative in the crib.

Getting out would help the rivals they deplore. Why not stick around—and prolong the gridlock?

This brings us, naturally, to Trump, the towering frontrunner (never mind that one poll this week that had Cruz overtaking him nationally), and the man responsible for setting the race’s current tone. To many Republicans, it was flabbergasting to hear Trump, in Saturday's debate, attack the Bushes in terms you might expect to hear from a Democrat, accusing W. of failing to protect America from terrorism and lying to draw the country into a disastrous war. Trump also had kind words for Planned Parenthood.

The most remarkable thing about Trump’s performance wasn’t that he took positions uncommon for a Republican, Brad Todd, a Virginia-based consultant who ran the super PAC supporting Louisiana Governor Bobby Jindal until his campaign ended in November, told me. It was that the putative frontrunner for the Republican nomination was making no effort to expand his appeal to other GOP constituencies by winning over his opponents’ supporters, as Political Strategy 101 would dictate after a big primary win. “Instead, he was more combative than ever before,” Todd said. “This is not a guy who’s trying to get to 50 [percent]. He’s trying to maintain the cult of Donald Trump, defined as being different from all these other people.”

Todd’s analysis reminded me of something Harris, the Rubio adviser, told me a couple of weeks back. The electorate, he said, was like a pie divided into different slices. But one of the slices was made of titanium—that was Trump’s share. It wouldn’t get much smaller, but it wouldn’t get bigger either. The others were all malleable and would grow as they merged.

Taking the metaphor too far, I pointed out that it’s difficult to unslice a pie. Harris considered this. “It’s a Key lime pie,” he said.

On Thursday night, after a day of media frenzy about Trump’s feud with the pontiff, I followed him to Gaffney, the town best known for its peach-shaped water tower, featured on the Netflix series House of Cards as the home of the fictional Frank Underwood. The Peachoid, as it’s known, could not be seen from the electric cooperative where Trump was scheduled to speak, a low-slung industrial building whose surrounding fields of tall, winter-brown grass were covered in parked cars. On the way in, I passed a man in a suit holding a poster reading “DONALD TRUMP IS A CHILDISH EGOMANIAC.”

If the race today has turned brutally personal, Trump is surely the reason. No one insults people like Trump, with a combination of humor and intense focus on some devastatingly intimate personal weakness: Jeb Bush is “low-energy,” Rubio wishes he were taller, Cruz is a liar. Trump pounds the accusation home until it becomes indelible—the only thing you can see when you look at his rival.

Bush, Trump told the audience, was “a nasty guy” who had spent $20 million on ads attacking him—but, he mused, perhaps he should actually be thanking him, since the attacks only seemed to strengthen Trump. Cruz, he said, “holds up his Bible and then he lies. That guy lies. He is a liar.” He claimed Cruz’s victory in Iowa was the result of fraud and should be invalidated.

The pundits all day had been wondering whether squabbling with the Pope—the Pope!—would hurt Trump. (There is, by now, a default pundit stance on Trump’s regular outrages, to wit: “This is deplorable, and Trump’s support will probably grow as a result of it.”) Interestingly, Trump’s instincts steered him away from the controversy. He didn’t mention Francis at all.

Trump recapped the debate. “I was being hit by everybody,” he said. “They’re desperate, they’re desperate. I thought I did really well. Although some of the pundits said, ‘He’s too nasty, he’s too tough.’ What, am I going to be nice? These people are shooting at me!”

A chant of “Trump! Trump! Trump!” went up from the crowd of thousands seated on folding chairs.

“Somebody said he was too tough, he was too nasty. Well, we’ve got to be nasty, folks. ISIS, they’re chopping off people’s heads! Oh, we’re going to be so nasty, folks. ISIS is not going to like us.”

On the way out, I spoke to 35-year-old John Jones, who had come to the rally with his mother, father, and sister. “If he don’t win, this country’s done. We’re over,” he said.

“The Pope is a nutcase,” his father, Harry Jones, volunteered. “All they are is a cult. They’re not Christians. He’s a zero. He’s a commie. He’s as useless as tits on a boar hog.” The Joneses are Baptists.

I thought back to Wednesday night in Spartanburg, where I had run into an Army Reserve officer named Dean Glossop in the parking lot of a Cruz town hall. Glossop was struggling to affix a homemade poster to the back of the cab of his gleaming gold F-150 pickup. It read “D. Trump: The ‘D’ is for Democrat! Don’t be Fooled!”

Glossop, who wore a Ronald Reagan Presidential Library sweatshirt and a USS Ronald Reagan cap, told me, “Any conservative who votes for Trump is just not listening. I don’t believe he has any more reverence for the Constitution than does President Obama.”

Quoting the Bible, Glossop said that he didn’t believe the end times were approaching, but he couldn’t be totally sure. He was not bothered by the current stalemate in Congress. “People who say they love bipartisanship and hate gridlock, that just means the rest of us get screwed,” he said.

Glossop and the Joneses were from adjacent parts of the same state. They were members of the same political party. But they did not seem to want to be on the same planet. Come this summer, if the Republican Party can’t figure a way out of its current mess, they may take their disagreement all the way to the arena in Cleveland.