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.