State attorneys say it would be very difficult but not impossible to move up a special election to fill the seat of former U.S. Rep. John Conyers.
A judge heard arguments Thursday on a request to set an earlier date.
Michael Gilmore, a candidate and lawyer, says the rights of 13th District residents are being violated by an 11-month gap without a member of Congress.
Conyers quit in December.
Gov. Rick Snyder ordered a primary election for August, followed by a general election in November. The winner would serve the remaining two months in Conyers' term.
Gilmore is proposing an earlier primary and then a general election in August. The winner would serve for five months.
Federal Judge Mark Goldsmith didn't make an immediate decision.