The rapidly-escalating political fight over resettling Syrian refugees has already reached the halls of Congress, where senior Republicans want to use a critical government-funding bill to force President Obama’s hand.

GOP lawmakers are reacting in predictable fashion to reports that at least one of the terrorists involved in the Paris attacks had slipped into the country with refugees fleeing the chaos in Syria. Fearing a similar plot in the U.S., more than a dozen governors (including one Democrat) quickly demanded that the Obama administration keep refugees out of their states. But the real battle may be fought on Capitol Hill over the next several weeks, with an aggressive Republican push that could result in a government shutdown.

The White House and congressional leaders are now negotiating an enormous omnibus spending bill that will appropriate funds for the next 10 months according to the budget agreement that passed in October. That legislation—or another temporary measure—must pass by December 11, when current funding expires. Senator Jeff Sessions, an immigration hard-liner from Alabama, on Monday sent a letter calling for more restrictions on the administration’s plan to admit more than 10,000 Syrian refugees into the U.S. over the next year, including a separate vote by Congress—which would never pass in the current political climate. “It is not sound policy to encourage millions to permanently abandon their homes,” Sessions wrote. “We have resettled 1.5 million migrants from Muslim nations in the United States since 9/11, and it clearly has not contributed to the stabilization of unstable regions.”

Sessions has never been a fan of either legal or illegal immigration, but he argued that the coordinated terrorists attacks in Paris on Friday “add immense new urgency.” A similar call came from the chairman of the House Homeland Security Committee, Representative Michael McCaul of Texas, who in a letter to Obama called for the suspension of the administration’s plan to admit more refugees pending a full review of the program. Representative Devin Nunes, the chairman of the House Intelligence Committee, also voiced opposition to the refugee policy in an appearance Sunday on “Face the Nation.”

Because of the extensive vetting process already in place, fewer than 2,000 refugees from Syria have been resettled in the U.S. And judging from Obama’s remarks Monday in Turkey, a push by Republicans to shut the door to more is likely to meet stiff resistance. The president denounced calls from Republican presidential candidates to admit only Christian refugees from the Middle East and reject Muslims as “shameful” and “un-American.” “We don’t have religious tests to our compassion,” Obama said.

The refugee debate poses an early challenge for the new House speaker, Paul Ryan, who said in an interview Sunday on “60 Minutes” (taped before the Paris attacks) that he thought he could strike an agreement with the White House to keep the government open. On Monday, he was noncommittal on the question of refugees. “We have always been a generous nation taking in refugees, but this is a unique situation,” he said in a radio interview with Bill Bennett. Asked specifically about using the funding bill to restrict refugee resettlements, Ryan said only that he had the House’s committee leaders to review the policy. “We’re looking at all of these options,” he said. “We’ve got to make sure we are protecting ourselves.” Senate Majority Leader Mitch McConnell will also have a big say in the refugee question, but he hasn't indicated where he stand. (A spokesman for McConnell did not return a request for comment on Monday afternoon.)

Ryan and McConnell will surely face pressure on refugees from the right flanks in Congress and from the presidential campaign trail. In perhaps the most outlandish statement of the day, Mike Huckabee tweeted that if Ryan did not "stop the importation” of those fleeing the Middle East, he should step down as speaker—less than two weeks after he formally took the job.

In the immediate aftermath of the Paris attacks, the politics seem to be shifting faster than the facts can be established. Was one of the attackers someone who posed as a refugee? That’s still unclear. A report on Monday afternoon from The Independent suggests that the passport belonging to the bomber in question may have been forged. And even if Republicans press forward with their refugee demand, it joins dozens of policy concessions they’ll seek to win in the upcoming spending fight, including restrictions on Planned Parenthood, environmental regulations, Obamacare funding, and more. What’s clear is that while keeping the government open never seems to be an easy job for Congress these days, the political fallout from the attacks in Paris might make it even harder now.