In late June, President Trump met with a dozen or so family members of Americans killed by undocumented immigrants as part of a push for two new laws targeting illegal immigration. “We’re calling on all members of Congress to honor grieving American families by passing these lifesaving measures in the House, in the Senate, and then sending them to my desk for a very rapid signature,” he said at the White House meeting, a day before the lower chamber approved both bills. “I promise you—it will be done quickly.”

Immigration restrictionist groups aren’t so sure about that promise, though they share the president’s desire to curb entries into the United States and force undocumented immigrants out. In their view, and in actuality, the legislation faces difficulty in the Senate, where lawmakers have been mired in a debate over health care and have plans to take up tax reform next. These advocates see the legislation, at best, as a path toward a broader, more stringent immigration measure. But at worst, the bills could be just another letdown.

Ahead of the June meeting, House Judiciary Committee Chairman Bob Goodlatte had introduced the pair of bills. One was Kate’s Law, which imposes tougher sentences on offenders who were previously deported and returned to the United States illegally. (It was named for a young woman, Kate Steinle, who was shot and killed by a man who’d been deported five times before reentering the country.) The other was the No Sanctuary for Criminals Act, which hits on Trump’s campaign promise to punish jurisdictions that limit their cooperation with federal immigration authorities. The bill cuts off some federal grants for these self-described “sanctuary cities,” like San Francisco where Steinle was shot. “The bills crack down on dangerous sanctuary policies that needlessly put innocent lives at risk,” Goodlatte said in a statement at the time.

The president touted their passage through the House as a victory. But like-minded organizations don’t seem to be keeping their hopes up. “There’s some sign of legislative life in the House and that’s very encouraging to us, but in the end, the Senate is where bills seem to go to die,” said Dan Stein, the president of the Federation for American Immigration Reform, which advocates for more immigration restrictions. “Considering the record of legislative achievement in the Senate, getting those passed would provide some assurance that something can get done.”

Stein’s group and others are growing frustrated with Trump, who made cracking down on illegal immigration the cornerstone of his presidential campaign. The president has so far come up short on multiple pledges—among others, his plan to immediately repeal the Obama-era Deferred Action for Childhood Arrivals program and another to seal off the entire U.S.-Mexico border. Trump’s assurances about the bills’ future seem to fit a larger pattern of overpromising on his agenda. And not just on immigration: “When we win on November 8th and elect a Republican Congress, we will be able to immediately repeal and replace Obamacare,” he said just before the election. “We will do it very, very quickly.” Months later, that still hasn’t happened, and Trump’s influence in Congress has often looked questionable.

So if any Trump supporters are looking to the Senate for a win on the two new bills, they’re unlikely to get it anytime soon. Senate Majority Leader Mitch McConnell has not said whether he’ll put Kate’s Law or the No Sanctuary for Criminals Act on legislators’ schedule, but the bills already look destined for Democratic pushback. Similar legislation has failed to advance in the Senate before. Another, slightly different bill known as Kate’s Law went down in a 55-42 vote last year. So did another sanctuary-cities measure. There’s little sign the new bills would have more luck securing Senate Democrats’ votes—especially when Trump’s anti-immigrant rhetoric seems to grow only more graphic.

Just three Democrats in the House supported the No Sanctuary for Criminals Act. While Kate’s Law received support from 24 of them in the lower chamber, their Senate counterparts don’t seem likely to follow suit. “Instead of criminalizing and scapegoating immigrants, Congress should be offering workable comprehensive reforms that actually strengthen our economy and national security,” said Democratic Senator Bob Menendez of New Jersey in a statement. “Until then, we will continue to be a firm wall of resistance—using all tools at our disposal—to prevent Republicans from blindly trying to sanction this administration’s mass deportation agenda.”

House Democrats who voted for Kate’s Law have already come under fire by Latino Victory Project, a group that supports Latino political candidates. “I think it’s shameful that these members, this handful of Democrats, decided to stand with Donald Trump instead of with Latinos and immigrants—instead of their own constituents,” Cristóbal Alex, the group’s president, said earlier this month.

Still, it’s not impossible that some Democrats could defect. As The Hill reported earlier this month, a “renewed push could force the 10 senators running for reelection in purple and red states won by Trump to take a tough, politically controversial vote.” In particular, Senate Republicans, who as a group have largely supported immigration-enforcement bills in the past, may look to Democrats like Joe Manchin of West Virginia for support. Manchin and two other Democrats up in 2018, Joe Donnelly of Indiana and Heidi Heitkamp of North Dakota, joined Republicans in voting for the 2016 Kate’s Law in the Senate. But it’s not clear what position they’ll take on the latest iteration.

Jonathan Kott, Manchin’s communications director, said the senator has “been focused on health care and hasn’t had a chance to review the bills yet.” A spokeswoman for Heitkamp expressed doubt about the legislation even coming to the floor: “The bills and amendments on this issue that have been voted on in the past in the Senate have all been different. Additionally, it’s still to be determined what bill, if any, will get a vote in the Senate.” (Donnelly could not be reached for comment.) Republicans would need at least eight Democrats to advance legislation.

Chris Chmielenski, the director of content and activism at NumbersUSA, is more optimistic than others about the bills’ potential. For one, he predicts there’s a “decent chance” McConnell will bring the sanctuary-cities bill to the floor. “Its prospects really depend on how much pressure [the] administration puts on those Democrats that are up for reelection in 2018,” said Chmielenski, whose organization supports reduced immigration. He has even greater confidence in Kate’s Law because of the publicity it received during the campaign and with Trump frequently invoking Steinle’s name and story.

“We don’t think [Kate’s Law is] necessarily an impactful piece of legislation, but because you did have 24 Democrats cross over party lines and vote with the Republicans on it—and because it does have some branding, it has some national name recognition—I think there’s a good chance that it’s going to come to the Senate floor,” he said. If it does, he thinks it has a chance at passing through the Senate.

Others have their doubts about Kate’s Law. “If only Kate’s Law passes, it changes almost nothing,” said Jessica Vaughan, the director of policy studies for the Center for Immigration Studies, which advocates for limiting immigration. “Just passing Kate’s Law is a tiny drop in the bucket of what needs to change. If they don’t pass the sanctuary bill, we’re going to continue to have a huge public-safety problem with sanctuary policies.”

For that same reason, Stein is concerned Democrats will vote for Kate’s Law, but not the sanctuary-cities bill, to stave off criticism from constituents. “We’re concerned that Kate’s Law might be viewed as political cover by some of the Senate Democrats who feel that the violent crimes committed by aliens who should’ve been deported or removed creates enough political liability that they need to take that vote,” Stein said.

Perhaps even more dire for the groups’ agenda is Congress losing its appetite for immigration legislation. “Of course our biggest concern is that ... they do pass the sanctuary cities bill, they do pass Kate’s Law through the Senate, and Trump signs them into law and then that’s it, no further action is taken,” Chmielenski said.

Immigrant advocates and civil-rights groups, meanwhile, have raised alarm over both bills. “The immigration enforcement approach championed by the Trump administration and embodied by Bob Goodlatte’s bills would harm, rather than help, public safety,” said Lynn Tramonte, the deputy director of America’s Voice Education Fund in a statement. “Despite the costs and consequences already on display throughout the country, House Republicans are poised to put the Trump administration’s existing cruel approach into overdrive.”

“I think generally we’re concerned that this represents the congressional implementation of Trump’s executive orders on immigration,” said Jose Magaña-Salgado, the managing policy attorney at the Immigrant Legal Resource Center.

For now, Trump’s immigration allies are waiting on McConnell. “If they miss this opportunity, [it’s] not a good sign for future legislation—then it looks like we’re condemned to bicker over issues endlessly without really changing anything,” Vaughan said.