Updated November 19, 2:00 p.m.

Republican leaders in Congress don’t want to kill the Syrian refugee program outright. But they may end up shutting it down anyway with a few added layers of red tape.

On a bipartisan vote of 289-137, the House on Thursday approved legislation aimed at “pausing” the resettlement of refugees from Syria and Iraq amid fears that ISIS terrorists could infiltrate the program after last week’s attacks in Paris. At first glance, the five-page bill appears rather perfunctory: It merely requires that three top national security officials—the FBI director, the secretary of Homeland Security, and the director of national intelligence—certify that each refugee is “not a threat to the security of the United States.” The legislation does not explicitly require the government to suspend the program, and a certification would seem to be a formality given that refugees already undergo extensive background checks that take as long as two years.

Politically, the goal is straightforward. Republicans kept the proposal narrow to attract Democratic support and show their constituents that Congress could, in a bipartisan way, tighten the refugee program without terminating it. The policy, noted House Speaker Paul Ryan, would judge refugee applicants only through the lens of security and would not distinguish between Christians and Muslims, like presidential candidates Jeb Bush and Ted Cruz have demanded. “We can be compassionate, and we can also be safe,” Ryan said on the House floor. “It would mean a pause in the program until we can be certain beyond any doubt that those coming here are not a threat. It’s that simple. And I don’t think it’s asking too much.” The House GOP proposal wasn’t aggressive enough for some conservatives, including Heritage Action and a few lawmakers who proposed amendments to suspend the program altogether.

But senior Democrats in Congress and their allies with refugee resettlement organizations have also come out in opposition to the bill, arguing that what Republicans insist is a “pause” will in practice cripple the refugee program for months or even years. The language in the bill, they say, will force the federal government to come up with an entirely new system of verification, and the resulting process could take so long that the security clearances that refugee applicants acquire will expire before they ever reach the United States. “Our concern is that this adds a huge layer of bureaucracy to an already bureaucratic process,” said Melanie Nezer, the chairwoman of Refugee Council USA who is also a vice president at HIAS, one of the nation’s nine resettlement organizations. “This is just going to cause delays that could take years.”

Nezer said the Republican message masked the true impact of the legislation. “If you look at all the ways they could shut down this program, this is a way to say this isn’t what they’re doing, but if you look at the legislation, that’s actually what the result is,” she told me.

Still, Republicans insisted the intent of the bill was not to end the program. “We’re not saying we’re refusing,” said Representative Michael McCaul, who introduced the proposal as chairman of the House Homeland Security Committee. “We’re just saying we want a thorough and robust vetting process before they’re brought in.”

“There are some that are saying, ‘Don’t bring in any on any basis whatsoever,’” McCaul added. “We’re not saying that.”

The other concern raised privately by Democrats is the fear of accountability in an inherently uncertain process. The nation’s top counterterrorism officials, they say, will blanch at the idea of personally certifying that each refugee is not a threat to the nation. As FBI Director James Comey—who would be required to sign off on individuals—acknowledged in congressional testimony last month, “there is risk associated with bringing anybody in from the outside, but especially from a conflict zone.”

The real worry is that nobody wants to be the person who vouched for a refugee if that immigrant ultimately does harm once they’re in the country, even years later. “It’s a way that will discourage, I think, anyone from taking a chance on anyone, even disabled children,” Nezer said. “Who knows what that child is going to grow up to be 50 years from now?”

Late Wednesday, the White House announced that President Obama would veto the bill if it reached his desk.

The certification requirement at the core of H.R. 4038 is untenable and would provide no meaningful additional security for the American people, instead serving only to create significant delays and obstacles in the fulfillment of a vital program that satisfies both humanitarian and national security objectives.

Yet the politics are tricky for Democrats. A Bloomberg poll released on Wednesday found strong public opposition to the resettlement of Syrian refugees, and despite the president’s lashing of Republicans on the issue, several Democrats have sided with the GOP. “A pause may be necessary,” Senator Charles Schumer, the chamber’s third-ranking Democrat, said on Tuesday. (He walked back those comments on Thursday.)

Nearly four dozen House Democrats voted for the Republican bill on Thursday, putting the measure just shy of the two-thirds majority needed to override a presidential veto. That increases pressure on Senate Minority Leader Harry Reid, who vowed on Thursday that the legislation would not clear the Senate. With Republicans needing only a handful of Democratic votes to break a filibuster, the challenge for the White House would then become holding enough Democratic support to sustain a veto. Critics of resettling Syrian refugees have the political momentum for the moment, and if that continues, the biggest threat to the program might come not from a group of protesting state governors, but from a Congress bent on slowing it to a halt.