Ballots postmarked before the polls closed at 7 p.m. on Election Day should be counted. Ballots with mismatched signatures should be counted. Ballots where voters made mistakes but where their intentions were clear should be counted. And deadlines to tally ballots in machine and manual recounts should be ignored.

Those are arguments lawyers for U.S. Sen. Bill Nelson, national Democrats and others are making as they have gone to federal court to try to help the long-serving lawmaker keep his Washington post.

With a machine recount underway and a manual recount looming in the close race for his U.S. Senate seat, Nelson and his supporters are racing against the clock while they try to convince a federal judge to toss Florida elections laws and nix a process laid out by Secretary of State Ken Detzner about the validation of “overvotes” in a manual recount.

Nelson trailed Republican Gov. Rick Scott by more than 56,000 votes on election night. But that deficit dwindled as ballots continued to be counted last week, especially in Democratic vote-rich Broward and Palm Beach counties.

By the time unofficial results were submitted to Detzner’s office at noon Saturday, Nelson trailed by fewer than 13,000 votes, prompting a statewide machine recount. If a similar margin comes out of the machine recount, the race will be thrown into a manual, or hand, recount.

The ballot counting has sparked lawsuits in federal and state courts, and the challenges keep on coming.

Nelson and supporters filed two more federal lawsuits Tuesday, two days before a 3 p.m. Thursday deadline for the machine recount to be completed and results to be submitted to  Detzner.

One of the lawsuits Tuesday asks the federal court to postpone the deadlines for the machine and manual recounts. Any manual recounts need to be finished by noon Sunday, with the state Elections Canvassing Commission — which includes Scott — certifying the official election results on Nov. 20.

Along with the U.S. Senate race, the races for governor, agriculture commissioner and three legislative seats are in machine recounts because of their narrow margins in unofficial results.

In arguing for abandoning the recount deadlines, Nelson’s lawyers pointed to Palm Beach County, where Supervisor of Elections Susan Bucher said she would not be able to complete the three statewide recounts as well as a recount in a state House race before Thursday. It also appears Bucher won’t be able to complete a manual recount for the U.S. Senate race by noon Sunday, Nelson’s lawyers wrote.

If counties can’t meet the deadlines, the most recent returns submitted to the state — following the machine recount or the election night totals — will be used.

“Given the extraordinarily compressed deadlines for completing a recount and the large number of races currently subject to machine recount, local elections officials are faced with a difficult task,” Nelson’s attorneys wrote in a 21-page complaint Tuesday.

The lawsuit focuses on a portion of Florida law that requires canvassing boards to submit official returns to Detzner no later than noon on the 12th day following the election, which is Sunday in this case.

“Where a county canvassing board remains in the midst of a manual recount, it obviously cannot truthfully make out such a certification. Florida’s ‘solution’ appears to be to disenfranchise voters whose votes remain uncounted in the name of administrative convenience,” the lawyers wrote.

In a separate lawsuit filed Tuesday, Nelson’s campaign and the Democratic Senatorial Campaign Committee asked a federal court to block a rule by Detzner that outlines the way ballots should be counted during a manual recount.

In a manual recount, county canvassing boards examine ballots with “undervotes” and “overvotes” that could not be tallied during a machine recount and determine which ones should be counted.

One of Detzner’s rules requires a voter to have marked all contests in the same manner for a ballot flagged as an undervote or overvote to be counted. That means that, if a voter circles a candidate in one race but uses an “x” to indicate her preference in another race, her ballot wouldn’t be counted, according to the 34-page complaint filed Tuesday.

Another rule provides that a voter who fills in a selection for a candidate, crosses it out and indicates with “magic words” that he or she made a mistake will have the ballot counted. But ballots in which voters did not give any written instructions indicating how they intended to vote will be rejected, under the rule.

The “magic words requirement operates to invalidate a vote even though the voter has clearly indicated her definite choice by crossing out, striking through, or scribbling out the erroneous choice,” Nelson’s lawyers wrote. “Without relief from this court, these voters will be deprived of their right to vote, and to have their vote counted, in the November election.”

On Monday, meanwhile, the VoteVets Action Fund, the Democratic National Committee and the Democratic Senatorial Campaign Committee filed a lawsuit challenging a state law requiring mail-in ballots to be received by county elections offices by 7 p.m. on Election Day.

Unlike regular mail-in ballots sent from within the U.S., ballots from overseas voters can be counted up to 10 days following the election, if they were postmarked by Election Day.

Determining the validity of ballots solely on a “received by” date, rather than pairing it with a postmark date, runs the risk of denying the right to vote based on “arbitrary factors” out of the control of Floridians, lawyers for the Nelson supporters argued in the filing.

In one case, a voter who lives in Miami-Dade County said he mailed his ballot a week before the Nov. 6 election, but learned later that his ballot had not been received in time, according to the lawyers.

In another lawsuit, Nelson’s lawyers are asking a federal judge to strike down a Florida law requiring elections supervisors to toss out provisional and mail-in ballots if voters’ signatures don’t match the ones on file.

U.S. District Judge Mark Walker will hold a hearing Wednesday in Tallahassee in that case.

During a telephone hearing Tuesday involving the vote-by-mail deadlines, Walker tried to figure out how quickly he has to decide in the matter.

Trying to set deadlines for briefs to be filed, the judge took note of the fast-approaching recount deadlines, along with the final certification slated for next Tuesday.

Saying he wasn’t “in any way telegraphing to either side what my view is on any of these cases,” Walker said, “ I know one thing for sure.”

“I need to rule on an expedited basis,” he said. “If that means we don’t sleep, that’s fine. But we all need to work hard to address these matters in a timely way. The people of Florida deserve that.”

Scott’s supporters have repeatedly characterized the Democrats’ lawsuits as attempts to “steal” the election.

“When the machine recount is complete on Thursday, Nelson will have to decide if he wants to preserve his legacy and go out with dignity or if he wants to be forever remembered as the guy that liberal interest groups used in an effort to win the presidential election two years early,” Scott’s campaign spokesman Chris Hartline said in a statement.