Minnesota's Democratic Party went to court Tuesday to demand that new absentee ballots be mailed to those who have already sent in their votes for Sen. Paul Wellstone, who was killed in a plane crash last week.
The state Supreme Court scheduled a hearing for Thursday.
The lawsuit was filed on behalf of Democratic chairman Mike Erlandson and two voters who will be out of the state on Election Day.
Wellstone was up against Republican candidate Norm Coleman in a tight race for the Senate when he was killed.
Absentee votes that were cast for Wellstone will not be given to the Democrat who runs in his place. That is widely expected to be former Vice President Walter Mondale.
Under the state's current plan, people already have mailed in their absentee ballots and want to change their vote would have to go to a local election office and request a new ballot. New ballots would not be mailed out, even for people unable to reach their election office.
The lawsuit seeks a court order allowing voters to have a new absentee ballot mailed to them promptly if they want to make a change.
The Democrats allege that the current plan, outlined by Secretary of State Mary Kiffmeyer, a Republican, and Attorney General Mike Hatch, a Democrat, "may well disenfranchise persons who may cast those ballots for Sen. Wellstone."
"They told us we're 'out of luck.' It's true we were out of luck last Friday when Senator Wellstone was killed," Democratic Party lawyer Alan Weinblatt said. "Why should we be out of luck on a continuing basis?"
The contest is seen as critical in control of the Senate, which Democrats now control by a single seat.
In response to the lawsuit, Kiffmeyer said officials "have and will address all legal and legitimate concerns to ensure that this election is properly administered and in accordance with the law."
Republican Party lawyers filed papers asking to intervene in the case, arguing that it could delay distribution of absentee ballots. They said any delay creates the "risk of being denied the right to vote" at all.
At least one county is breaking ranks with the state plan. Officials in Ramsey County, which includes St. Paul, said they will mail a new ballot to those who ask.
"We're not going to question someone as to why their ballot is spoiled," said Darwin Lookingbill, director of the county attorney's civil division. "If they call we're going to send them another ballot."