TALLAHASSEE — Florida's system of reviewing voters' signatures on mail ballots is on trial in a federal courtroom as Democrats and Sen. Bill Nelson try to expand the pool of potential votes in his razor-close Senate race.

U.S. District Judge Mark Walker heard testimony and arguments for five hours Wednesday in Nelson's lawsuit that seeks to count thousands of mail and provisional ballots that were disallowed, because the voters' signatures on ballot envelopes didn't match the signatures on file.

Walker did not rule in the case, but a decision is imminent as 67 counties must complete machine recounts by 3 p.m. Thursday.

As the hearing ended, Walker urged state elections officials to give him a precise accounting of how many ballots have been rejected because of signature problems.

A report from 45 counties produced in court Wednesday showed 3,688 rejected mail ballots and 93 rejected provisional ballots. Walker made it clear that's not good enough.

"Let's be as transparent as we can and provide as much information as we can," Walker told attorneys for Scott's chief elections officer, Secretary of State Ken Detzner.

The names of the candidates, Nelson and Republican Gov. Rick Scott, who holds a 12,562-vote lead, were barely mentioned, but the political stakes were obvious to everyone in the courtroom — especially the judge.

"Apparently I'm supposed to re-evaluate the entire election code of the state of Florida, one piece at a time. I've got it," Walker said. "This just seems like a really bad way to do this."

Nelson, playing catch-up against Scott in his final campaign of a five-decade career in politics, has filed a flurry of lawsuits.

They seek to include disputed mail and provisional ballots in vote tallies, extend vote-counting deadlines and invalidate the state's definition of voter intent in deciding whether under- and overvotes are legitimate.

In Wednesday's case, Nelson argued that a state law that rejects ballots with mismatched signatures is inconsistent and unreliable and violates the equal protection clause of the U.S. Constitution.

Nelson's lawyers say signatures change over time for a variety of reasons, including age, illness, injury, medicines, eyesight, alcohol and drug use.

Walker has issued several rulings in elections cases that are on the side of expanding voting rights while critical of Scott's administration.

"Look at this through the prism of a person who was disenfranchised," he said Wednesday, referring to the efforts it took for women and blacks to gain the franchise. "My ancestors weren't held in chains."

There was more criticism Wednesday after lawyers for Scott's elections division and for Attorney General Pam Bondi argued that Nelson had no legal case because he waited too long to file a lawsuit, and that voting by mail is not a constitutional right, but a privilege.

Walker, his voice rising, told one of Bondi's attorneys: "If that's your theory, we'd still have segregated schools in Florida."

The judge appeared to float a compromise that would allow any vote-by-mail voter whose ballot was rejected due to a signature mismatch to challenge that decision. At one point, Walker suggested a three-day challenge window, which Nelson's lawyers said was too short.

State and county officials are working under extraordinarily tight time deadlines. Manual recounts are expected to be ordered Thursday in the races for Senate and agriculture commissioner.

Manual recounts of hundreds of thousands of undervotes and overvotes must be completed by noon Sunday, and final results are expected to be certified next Tuesday.

Early on Wednesday, Walker sent a strong signal that he would not give Nelson the answer he was seeking.

"Why in the world would I say 'Count them all' without regard for whether they are valid votes?" he asked Nelson's team of dark-suited attorneys.

Walker then quoted an ancestor: "My grandfather would say that's roughly akin to hunting squirrel with a bazooka."

The judge appeared swayed by Mark Earley, the elected supervisor of elections in Tallahassee's Leon County, who testified about how the signature verification process really works.

Election workers compare a voter's signature on a ballot envelope against their original voter registration application, the signature on a driver's license or a digital signature on an electronic pad at a polling place.

Earley said canvassing boards review signatures closely, but rarely reject ballots. Of the 27,301 people who voted by mail in Tallahassee, he said, 38 ballots were rejected for mismatched signatures.

"We look at the signatures very carefully. We are trying to find matches," Earley testified.

He also testified that Leon counted 25 ballots as valid even though the affidavits from voters attesting to their identities never reached the elections office because of a delay by postal employees.

"That seems like a pretty thorough process to be sure every vote's counted," Walker said. "It was pretty impressive."