The Obama administration has a big Syrian refugee problem.

The House of Representatives just voted to approve a bill that would allegedly require three top administration officials, including the FBI director, to approve every individual Syrian refugee asking to enter the US. The administration argues that the bill would essentially stop America from taking in any Syrians at all. But it can't even convince members of the president's own party: The bill passed the House with a veto-proof majority.

Related How the US screens Syrian refugees now

Even if Senate Democrats hold the line against a veto override, that won't permanently solve the problem. It's looking extremely likely that congressional Republicans will demand changes to Syrian refugee policy as a condition for keeping the government open past December 11. And unlike past shutdown threats, this is one congressional Democrats might actually go along with.

For congressional Republicans, this bill is a brilliant strategic move. It's anodyne enough that it's attracted broad support from congressional Democrats as well as Republicans. And it's forced the Obama administration — which has never had good relationships with Democrats on Capitol Hill — to fight an uphill battle.

The bill would require the Department of Homeland Security secretary and the FBI director to sign off on each individual refugee

The bill the House passed, which is called the American Security Against Foreign Enemies Act (or the American SAFE Act, because Congress has a cutesy-acronym problem), requires the federal government to set up a new process, on top of the background and security checks it currently conducts, to "certify" individual refugees from Syria and Iraq before they're allowed into the United States.

The bill doesn't spell out exactly how the certification process is supposed to work — it leaves that to the government. All it says is that every time the US considers admitting a refugee from Iraq or Syria, the FBI director has to swear to the Department of Homeland Security secretary and the Director of National Intelligence that the refugee has passed a "sufficient" background check — and then the three officials all need to certify that the refugee is not a threat to US security.

The bill doesn't directly force the US to stop processing applications from refugees in Syria and Iraq. But in practice, both its supporters and its opponents agree that it would result in the refugee process being paused while the relevant government agencies worked out how the certification process would work in practice. Opponents of the bill say that it's likely to take months for three different federal offices to agree on standards for certification. (Supporters don't contest this, but in the words of Speaker Paul Ryan, "time isn't the issue; quality is the issue.")

Once the certification process was set up, the government could start processing Syrian (and Iraqi) refugees again. But it would almost certainly take even longer to vet and approve refugees than the 18 to 24 months it takes now.

The way the Obama administration and previous administrations have interpreted federal law, when a law says that a Cabinet secretary (or other official) has to certify something to Congress, it means that official has to personally sign off on it. By that interpretation, under the American SAFE Act, DHS Secretary Jeh Johnson, FBI Director James Comey, and Director of National Intelligence James Clapper would all have to personally sign off on each individual Syrian or Iraqi refugee.

In October 2015, the government admitted 187 Syrian refugees into the US. At that pace, the US would admit about 2,200 refugees during fiscal year 2016 — far, far fewer than the 10,000 the Obama administration has said it wants. But it would still require Johnson, Comey, and Clapper to sign off on six refugees a day.

Obama thinks this will maim the refugee process. Congressional Democrats aren't convinced.

Politically, the response to the bill is something that hasn't been common over the past couple of years: Republicans are united, and Democrats are split.

Because the American SAFE Act doesn't completely freeze Syrian refugee admissions — and because, just like the current system, it relies on the Obama administration to determine when refugees are a threat — its support among hard-line conservatives wasn't guaranteed. But they appear to be on board. According to reports, when Rep. Louie Gohmert (R-TX) announced he'd support the bill, his fellow Republicans cheered.

Democrats are showing no such unity. On one hand, President Obama has already promised to veto the bill if it reaches his desk, and the minority leaders of the House and Senate are both condemning it as an assault on refugees. But a few hawkish Democrats (including Sen. Chuck Schumer, the likely next Democratic leader of the Senate) have been open to pausing Syrian refugee admissions. Most Democrats appear to be somewhere in the middle: They want to help Syrian refugees, but they don't have a problem with this bill.

The Obama administration's underlying problem is that it has never had a good relationship with congressional Democrats. This is far from the first time that Democrats on the Hill have split with the administration (see most recently the Trans-Pacific Partnership). So the administration has no chance of persuading House Democrats worried about reelection that it's worth it for them to take a hit and risk ads all over their district saying that they "voted to let terrorists slip into the US" on President Obama's behalf.

Compounding this, the American SAFE Act isn't, on its face, all that different from existing policy. The Obama administration has sworn up and down that it already subjects would-be refugees to exhaustive security checks. Asking for formal certification doesn't seem like a big deal. The administration believes it would be a massive pain to require the DHS secretary to sign off on individual refugees, but that is not a terribly persuasive argument — especially for Democrats who don't always respect the administration to begin with.

Republicans can drive a wedge between the White House and congressional Democrats — if they stay disciplined

Congressional Republicans have struggled to stay unified and disciplined over the past few years, with the result that the most politically conservative and tactically radical Republicans define the party. But pushing the American SAFE Act is a very savvy move.

It gives Republicans what they want on policy: The administration admits that the bill would, in practice, pause Syrian refugee admissions. But a bill that explicitly called for the administration to stop admitting Syrian refugees might galvanize Democrats in defense — and open up Republicans to accusations of racism.

Instead, they've designed a bill whose text is pretty unobjectionable-sounding. As a result, the administration is in the unenviable position of trying to persuade distrustful Democratic members of Congress to trust the administration when it says the bill is worse than it sounds — so bad, in fact, that they should risk being portrayed as "soft on terror" in the next election cycle.

For the moment, at least, the administration has failed so completely to persuade House Democrats that the bill could — at least in the House — override the president's veto if it had to. The question is whether Senate Democrats will side with the House or the White House. If the resounding support for the American SAFE Act on the House side persuades enough Senate Democrats to defect, Obama will have a serious problem on his hands.

If Senate Democrats hold the administration line, Obama won't even have to follow through on his veto threat; they can filibuster it to death. But there's another government funding deadline coming up December 11, and some congressional Republicans have been calling — even before the American SAFE Act was introduced — for Congress to shut down the government if Obama hasn't taken action on Syrian refugees.

The American SAFE Act has shown that — unlike the past few government shutdown fights, on the Affordable Care Act and Planned Parenthood — Democrats aren't necessarily committed enough to the current Syrian refugee program to vote against a funding bill that would change or end it. That could pose a very big problem for the administration.

But before Democrats have to make a choice between keeping the government running and accepting changes to refugee policy, Republicans have to figure out what they're going to ask for. And there's nothing requiring them to stick to the SAFE Act. They could demand that Syrian refugee admissions be stopped entirely in exchange for keeping the government open. They could make demands on other issues as well; they could try to defund Planned Parenthood again, for example.

The more Republicans ask for, the more likely they are to unite Democrats in opposition. But if they keep their demands limited to things they know many Democrats support, they could easily strip President Obama of cover from Congress. He would have to choose: Would he be willing to directly veto a must-pass government spending bill and risk shutting the government down through Christmas and the end of the year? Or would he be willing to accept defeat, even if it means the US won't take in any more refugees from the worst conflict on Earth for the rest of his term?