Legal battles over voting laws are poised to play a decisive role Tuesday in some states with tight races.

Controversial statutes in Arizona and North Dakota have been challenged in federal court in recent months, with judges handing down rulings that are expected to keep thousands of voters from casting a ballot on Election Day.

And while voting rights groups were able to get relief for Georgia voters in high-profile disputes over the state’s “exact match” registration verification process, the courtroom drama has catapulted a hotly contested gubernatorial race into the national spotlight. If elected, Stacey Abrams (D) would become the first black female governor in U.S. history.

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Edward Foley, director of the Election Law program at Ohio State University’s Moritz College of Law, said voting procedures perceived to be hostile to minority voters have backfired in the past.

“It can actually increase turnout among groups that are purportedly targeted,” he said.

Voting rights groups say the exact match verification process disenfranchises minorities, who traditionally vote Democratic.

Federal district court judges have ordered Georgia Secretary of State and Republican gubernatorial nominee Brian Kemp, who is white, to give more than 51,000 voters a chance to prove their citizenship after they were initially deemed ineligible. His office was also told to stop tossing out absentee ballots and applications for voters whose signature does not match the one on the state’s voter rolls without giving voters a chance to correct the discrepancy.

Polling analysis website FiveThirtyEight on Monday showed Abrams leading Kemp by 4 percentage points, 50 percent to 46 percent. If neither candidate exceeds 50 percent on Tuesday, the state will hold a runoff election on Dec. 4.

A narrow margin of victory by either candidate on Tuesday would likely spark renewed scrutiny of the federal court cases and the state’s exact-match law.

In North Dakota, Native Americans are challenging a residential street address requirement in the state’s voter ID law in two separate lawsuits. They were unsuccessful in their efforts to block the law before Tuesday.

The 8th Circuit Court of Appeals blocked an initial win by Native Americans in the lower court that allowed voters to show a residential street address or valid P.O. box. The Supreme Court later refused to toss out the 8th Circuit’s ruling.

Native Americans went back to court to ask for more targeted, temporary relief for eligible voters who live on reservations but lack a valid street address.

Chief Judge Daniel Hovland, of the U.S. District Court for North Dakota, however, denied the group’s request last week, saying it was too close to the election to change the law.

“Courts try as best they can to get a valid voting system in place before ballots are cast but … sometimes lawsuits get filed and issues emerge too close to when the voting begins,” Foley said.

North Dakota’s law could keep hundreds of Native Americans, who voted overwhelmingly for Sen. Heidi Heitkamp Mary (Heidi) Kathryn HeitkampCentrists, progressives rally around Harris pick for VP 70 former senators propose bipartisan caucus for incumbents Susan Collins set to play pivotal role in impeachment drama MORE (D) in 2012, from casting ballots on Tuesday. Heitkamp is considered one of the most vulnerable Senate Democrats, running for reelection in a state President Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE won by 36 points in 2016.

And in a small-population state like North Dakota, even a few hundred votes carry a lot of weight.

Polls show Heitkamp is trailing her GOP challenger, Rep. Kevin Cramer Kevin John CramerMomentum growing among Republicans for Supreme Court vote before Election Day On Paycheck Protection Program, streamlined forgiveness is key McConnell shores up GOP support for coronavirus package MORE, in the polls. The nonpartisan Cook Political Report, an election handicapper, says the race “leans Republican.”

To take control of the Senate, Democrats need to successfully defend all of their seats and pick up two from Republicans. A component of that narrow path to victory includes the Senate race in Arizona, where Democrats are trying to pick up the seat being vacated by Sen. Jeff Flake Jeffrey (Jeff) Lane FlakeJeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Republican former Michigan governor says he's voting for Biden Maybe they just don't like cowboys: The president is successful, some just don't like his style MORE (R).

In that race, Democratic Rep. Kyrsten Sinema is facing off against Republican Martha McSally Martha Elizabeth McSallyTumultuous court battle upends fight for Senate Grassley, Ernst pledge to 'evaluate' Trump's Supreme Court nominee The Hill's Campaign Report: Biden goes on offense MORE and the Cook Political Report lists it as a “toss-up,” meaning the winner could be decided by just a few thousand votes.

The American Civil Liberties Union (ACLU) says hundreds of thousands of people may not be able to vote Tuesday because of the state’s alleged failure to update voter registration addresses when people changed information on, applied for or renewed their driver’s licenses.

The ACLU, which brought a lawsuit on behalf of the League of Women Voters of Arizona and two other voting rights groups, argues the secretary of state has violated the National Voter Registration Act, leaving voters unable to cast a ballot at their new or old polling locations.

A federal district court judge denied the ACLU’s request for a court order requiring the secretary of state to notify voters who may be affected and to count provisional ballots of those voters regardless of whether they are cast at the person’s new or old polling place.

Arizona argued that such an order could allow an estimated 63,000 people to vote twice on Tuesday.

Because the voter registration deadline had not yet passed when the ACLU filed its lawsuit in August, the group hopes it raised enough awareness among voters about the registration issue.

But Sarah Brannon, managing attorney with the ACLU Voting Rights Project, said there’s probably still a number of people in Arizona who have moved and did not have their voter registration updated.

“They will have a harder time voting,” she said. “A lot of people vote by mail, so the concern is that their mail-in ballots were not being sent to the right address.”