Senate Majority Leader Harry Reid (D-Nev.) and Minority Leader Mitch McConnell (R-Ky.) said on Wednesday that they would try to work out a Thursday vote on a House measure that would extend unemployment insurance, a move that would signal the end of the week’s lame-duck session.

Reid filed for cloture Wednesday evening on a bill that would extend unemployment insurance benefits after he failed to get unanimous consent for an economic stimulus package that included infrastructure funding, state aid for Medicaid, and a loan for the ailing automotive industry.

Republicans objected to all three bills.

The cloture petition guarantees there will be a vote on unemployment benefits by Friday, but Reid and McConnell are hoping to move that vote up by a day, and they said they would go back to their colleagues to work out an agreement that would allow a Thursday vote.

If the Senate succeeds, there is no reason for the House to come back to town because it has already passed the measure.

One Democratic leadership aide said a Thursday vote is very likely now that Reid is pushing only for the unemployment insurance, which has significant Republican support.

“They want to leave. A vote could happen as early as Thursday,” the aide said.

Reid tried all week to persuade Republicans to give the Big Three American auto-makers a $25 billion loan, but ran up against stiff opposition from President George Bush and GOP Senators.