Senate Majority Leader Mitch McConnellChip Somodevilla AFP/Getty

Last week, after House Speaker John Boehner announced his resignation, uber-conservative Sen. Mike Lee received a text from a congressman of a similar ilk: "Next guy in the crosshairs will probably be McConnell.”

The senator’s text back to Rep. Matt Salmon of Arizona: "Doubt about that conclusion.”

Senate Majority Leader Mitch McConnell is not Boehner, colleagues say, as his support from fellow Republicans in his chamber is much stronger. And yet outside groups are trying anew to bring him down, motivated by the fact that the tea-party movement has now claimed its most-prized scalp—and can sell its victory for a greater fundraising haul.

The Tea Party Patriots have set up a petitioning website to Fire the Leader; the super-PAC arm of the Senate Conservatives Fund is enticing its followers to vote in support of their own petition with “Ditch Mitch NOW!” bumper stickers. An article reporting that the chairman of the Louisiana Republican Party and a vice chairman of the Republican National Committee have called for McConnell to resign tops The Drudge Report; Gov. Bobby Jindal agrees. Right-wing radio is abuzz; Laura Ingraham said in the hours after Boehner’s ouster that the “next question” is when McConnell will join him.

But the desire to fire appears to be coming entirely from the outside. The most senior GOP senator—Orrin Hatch of Utah—told National Journal that there are maybe two GOP senators who would want to knock over McConnell. The most obvious candidates, Lee and Sen. Ted Cruz, don’t seem to be taking the bait so far.

“The Republican leaders in both houses of Congress should actually lead,” Cruz said outside the Capitol on Monday night. “They should stand and fight for conservative principles. Neither Leader McConnell nor Speaker Boehner has been willing to do so.

“I believe conservatives deserve a leader in the Senate and a leader in the House who take seriously the promises we made to the voters,” he added. “Whether that is Mitch McConnell or somebody else is a decision for the Republican conference to make.”

The outside groups’ effort is “not going to go anywhere,” according to Hatch. “They don’t have that kind of swat in the Senate.”

He added: “I’ve had excellent leaders in the Republican party in the Senate. Over the years, I’d say [McConnell] ranks right at the top."

Sen. John McCain of Arizona, who has served alongside McConnell for nearly 30 years, said Monday that McConnell will continue to lead in part because of the stark differences between the House and Senate. “Senator McConnell has solid support amongst the Republicans in the Senate. The way we do things here, because there are a fewer number—there’s 54 of us, we all have these close, personal relationships, with the exception obviously of, you know, Ted Cruz, etc.—but I just don’t see that happening. He was unanimously elected our leader. There’s never been anybody who’s tried to undermine him.”

“There is no other choice,” added Sen. Rand Paul of Kentucky on Fox News Monday. “There is no election. There is no battle going on.”

Part of McConnell’s staying power, too, is a difference in personality. In the months leading up to Boehner’s resignation, rumors echoed through the halls of Congress and along K Street that the speaker had had enough. After five years of fighting tooth-and-nail with conservatives in his party and with another coup attempt on the horizon, it seemed clear that Boehner would rather step down and enjoy a few games of golf. Let the prisoners find a new warden and see if anything changes.

McConnell, though, is living his dream as majority leader, and despite hiccups and the occasional dustup with the much smaller faction of conservative members in the Senate, that pleasure doesn’t seem to be waning. “Mitch loves the game,” McCain said. “One of the reasons why he’s so successful is he plays a great game of inside baseball. And he loves it, you know? He likes to move pieces around the chess board, and he does it very well.”

“I think the only way he’s leaving is feet-first,” McCain quipped.

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