Tallahassee, Florida (CNN) The federal court hearing in Florida on whether to count thousands of rejected mail-in and provisional ballots concluded on Wednesday after more than five hours without a decision from Judge Mark Walker.

Florida law requires signatures on vote-by-mail and provisional ballots match the signatures on file for each voter. Attorneys for Democratic Sen. Bill Nelson's re-election campaign argued that Florida's signature-match rules violate the US Constitution and called for the judge to invalidate the law. Lawyers representing the state of Florida and the National Republican Senatorial Committee, along with others, argued that the law was valid and constitutional.

Walker did not rule from the bench on Wednesday and gave no timeline for a ruling, but he engaged all the parties in an extensive question and answer session, using lively language and hypotheticals to attempt to puncture each side's arguments. At times, he appeared skeptical of arguments on both sides.

The judge did indicate that he is unlikely to remove the state signature requirement, which would allow the now-voided ballots to be counted. Instead, he suggested finding a way for voters whose ballots had been rejected because of signature mismatches to address the problem through their local election officials.

Time is, however, of the essence, given a Thursday deadline for state election officials to finish the machine recounts of three statewide races, including Nelson's bid for re-election against Florida Republican Gov. Rick Scott and a final November 20 certification of all the election results.

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