By Devan Cole, CNN

(CNN) -- A federal judge in Texas is considering a GOP-led challenge Monday seeking to invalidate nearly 127,000 drive-thru ballots cast in the Democratic-leaning Houston area.

The lawsuit is a major last-minute challenge to voting rules in closely watched states ahead of the election, in which some officials have made special accommodations amid the coronavirus pandemic.

Sunday, the Texas state Supreme Court denied a similar petition on drive-thru ballots. Roughly 10% of the votes cast in person during the early voting period have been cast at those sites.

In a separate case in Nevada, a judge rejected a Republican lawsuit seeking to halt early counting in Clark County, which includes Las Vegas, over the stringency of signature-matching computer software and how closely observers can watch votes being counted.

President Donald Trump and Republican officials have repeatedly made baseless claims of voter fraud and sought to cast doubt on measures including voting by mail and the use of dropboxes.

The hearing began at 10:30 a.m. CT, but public access has been limited.

Reporters and other members of the public were granted access to a teleconference about an hour after the hearing began. A phone line that had been set up for access broke down as the hearing was about to begin. Reporters inside the courthouse were held in the lobby and not allowed into the courtroom due to social distancing measures put in place due to the coronavirus pandemic.

About 90 minutes after the hearing began, those reporters were eventually allowed into the courtroom.

"Like so many 11th-hour voting-related suits filed by Republicans in recent weeks, this suit has almost nothing to do with voter fraud," Steve Vladeck, CNN Supreme Court analyst and professor at the University of Texas School of Law, wrote in an op-ed published in The Washington Post.

"Rather, it's the latest in a consistent and cynical line of suits -- in Wisconsin, Pennsylvania, Minnesota, among others -- that appear motivated by partisan gain, assuming that the exclusion of any set of ballots from Harris County ... is good for Republicans."

Judge is no stranger to controversy

Judge Andrew Hanen will hear the Houston challenge. Hanen was appointed to the bench in 2002 by then-President George W. Bush and now serves in the Houston Division of the Southern District of Texas, which sits in Harris County, the state's most populous county and a Democratic stronghold.

Hanen is no stranger to controversy. Back in 2016 he blocked President Barack Obama's push to expand the Deferred Action for Childhood Arrivals program as well as another program aimed at parents of legal immigrants. At one point as a part of that litigation, he was infuriated by actions taken by lawyers at the Department of Justice, causing him to issue a 29-page order that began by quoting a scene in the movie "Bridge of Spies."

Hanen also quoted from "Miracle on 34th Street" before concluding by ordering the attorneys who appeared in plaintiff states to go through a legal ethics course.

The case Hanen is set to hear Monday concerns 10 drive-thru voting locations Harris County set up for early voting, which ended Friday, and Election Day. The 10 locations are connected to traditional polling locations.

While curbside voting in Harris County is limited to voters with a disability and located at all polling sites, the drive-thru voting locations are open to all voters.

The federal challenge argues that drive-thru voting violates the US Constitution, which says state legislatures decide how elections are run. The plaintiffs also argued it violates the equal protection clause of the 14th Amendment, in that the county is adopting a manner of voting that has not been adopted by other Texas counties.

Jared Woodfill, a Houston lawyer representing the plaintiffs, argued that Harris County Clerk Chris Hollins was acting on his own by implementing the practice of drive-thru voting, but Hollins has staunchly defended the practice of drive-thru voting, calling it a safe and legal option amid the pandemic that's been repeatedly backed by the courts and election officials.

Hollins told CNN's Jim Sciutto on "Newsroom" Monday that should the nearly 127,000 ballots be invalidated, the county is going to use all available resources to reach out to the voters impacted by the decision.

"We are prepared to marshal all county resources, including emergency response technology, to reach out to 127,000 of the potentially affected voters," he said. "We do have tomorrow, Election Day, and we're going to do whatever we can to get them out there and make sure that their voices are heard and that their votes are counted."

On Sunday, the American Civil Liberties Union and the ACLU of Texas, representing several people who used the drive-thru option in Harris County, filed a motion to intervene in the case on behalf of the county.

Joy Davis-Harasemay, a 44-year-old Houston voter who is one of the Texans named in the motion, has "both asthma and spondylitis, a degenerative spine disease that makes her unable to stand for long periods of time," according to the ACLU, which argued she would be disenfranchised if the votes are invalidated.

"The push to toss the ballots of nearly 127,000 Texans in Harris County is unconscionable and illegal," Sophia Lin Lakin, the deputy director of the ACLU's Voting Rights Project, said in a statement. "It appears to be an attempt to undermine a true and accurate vote count and improperly influence the outcome of the election."

This story has been updated with details from the hearing.