It’s that time again. The last bill to fund the federal government expires on September 30th. If Congress doesn’t pass new funding legislation by then, much of the government will shut down.

Republican House Speaker Mike Johnson, spurred on by the House Freedom Caucus and former President Donald Trump, reportedly wants to use this deadline to push through a law that would make voter registration more difficult in all 50 states.

Johnson plans to combine a bill to fund the government for six months with a Republican bill called the Safeguard American Voter Eligibility Act (SAVE Act), which would require new voters to provide “documentary proof of their U.S. citizenship,” such as a passport or birth certificate, to register to vote.

There is no evidence that noncitizens participate in U.S. federal elections in significant numbers, and states typically have protections in place to prevent them from doing so. For example, Georgia’s Republican Secretary of State Brad Raffensperger claims he identified 1,634 “potential noncitizens” who wanted to register to vote over a 15-year period. But these potential noncitizens were caught by election officials and never registered. In 2020, nearly 5 million Georgians voted in the presidential election.

More generally, according to the Bipartisan Policy Center, “Illegal registrations and attempts to vote by noncitizens are routinely investigated and prosecuted by appropriate state authorities. There is no evidence that attempts by noncitizens to vote were serious enough to affect the outcome of an election.”

Although noncitizen voting—which is, of course, illegal—has never been proven to influence an election, there is evidence that the SAVE Act could influence elections. This is evident in Arizona, which already has a system similar to the SAVE Act in place. Data from Arizona suggests that the state’s law has made it somewhat harder for people of color, a group that tends to lean Democratic, to vote. And at least one analysis of Arizona voter data suggests that the SAVE Act may suppress voter registration of another group that tends to lean Democratic: college students. So the law could make it somewhat harder for Democrats to win elections.

However, the SAVE Act contains a vague provision that allows voters who “cannot provide” the required documentation to provide other proof of their U.S. citizenship, and requires state or local officials to “determine whether the applicant has adequately established U.S. citizenship.”

It is unclear what exactly this means.

Notably, the SAVE Act would take effect immediately if passed by Congress, and it would impose significant new administrative burdens on state and local election offices. So if the law were to take effect in the two months before a presidential election, it could potentially throw that election into chaos.

Realistically, this outcome is unlikely. Axios reports that Republican Senate Minority Leader Mitch McConnell is opposed to making continued funding for the U.S. government contingent on the passage of the SAVE Act. Most Democrats and President Joe Biden are also against the bill.

Still, the fight over the SAVE Act could put the United States at risk of a government shutdown. And while the SAVE Act is unlikely to become law in the next two months, it is likely to be on the list of bills that Republicans will be keen to pass if they win the November election.

If the SAVE Act becomes law, it would likely have little impact on election outcomes—though even a minor change in voting eligibility could potentially affect very close elections, especially in swing states. On its face, the bill addresses a non-issue—there are no legitimate concerns about noncitizens voting in the United States. And most voters have documents that would allow them to register under the SAVE Act.

Still, Arizona offers a useful glimpse into voting opportunities under the SAVE Act. In 2004, the state passed a law similar to the SAVE Act that requires new voters to show proof of citizenship when registering. But that law conflicts with a federal law that requires states to register voters who file a standardized federal form. In 2013, the Supreme Court ruled that Arizona cannot exclude voters who register using that form from participating in federal elections.

However, Arizona responded to this decision by creating a second-class voter system. Arizona voters who file the federal form without documentary proof of their citizenship are allowed to vote in federal elections (for Congress and President), but not in state elections.

Data from Arizona suggests that non-white voters (who tend to favor Democrats rather than Republicans) are more likely to be registered as federal-only voters than white voters. But college students appear to be hit hardest by Arizona’s two-tier system.

A report by Votebeat, a news outlet that covers election administrations, found that most precincts in Arizona have fewer than a dozen voters totaling federal-only ballots. But “of the 12 outliers with more than 300 federal-only ballots,” Votebeat reports, “all but one are at least partially located on a college campus.” The lone exception was a precinct in Phoenix that is home to a homeless shelter.

This conclusion is intuitive. College students who leave home to pursue their degrees often do not bring their passport or birth certificate with them to school and thus cannot present them when registering to vote. (People without permanent residence also likely do not have immediate access to these documents because they do not have a home in which to store them.)

If the election result is close, a law that disenfranchises many college students could be the deciding factor.

In the razor-thin election of 2000, for example, official counts showed that President George W. Bush won the crucial state of Florida by 537 votes. Meanwhile, the University of Florida alone has nearly 35,000 students enrolled.

So even if the SAVE Act would not do much to solve the alleged problem of non-citizen voting, it would at least have some impact on U.S. elections.