Senate Majority Leader Harry Reid (D-Nev.) has scheduled a vote for Thursday to proceed on a measure related to the country’s debt – a can’t-miss vote for most members.

The timing of the vote? Right after Obama’s 7 p.m. jobs speech.

Reid’s move means that the few Senate Republicans who had planned to skip town Thursday night are now reconsidering their options.

Sen. David Vitter (R-La.), who had sent an e-mail to supporters Wednesday trumpeting his decision to skip the speech and host a New Orleans Saints party instead, said Thursday that he would remain in Washington for the speech and vote – but he was not pleased to be doing so.

In a second e-mail to supporters and in messages on Twitter and Facebook, Vitter accused Reid of playing politics by scheduling the debt vote for Thursday night.

“Typical Harry Reid,” Vitter wrote to supporters in a message with the subject line, “More Scheduling Hijinks.” “He’s now scheduled votes that should’ve been held this morning for right before and right AFTER prez’s speech. Pens in those who would have skipped speech, like me. So now I’ll miss my own Saints game party at home. Always knew Harry was a Dirty Birds fan! Don’t worry — only strengthens my Who Dat resolve. On to the Super Bowl!”

The Saints face off against the Green Bay Packers on Thursday night in the NFL season opener, shortly after Obama’s speech. Vitter and Sen. Jim DeMint (R-S.C.) as well as a handful of House Republicans had announced that they would be skipping Obama’s address; a DeMint spokesman did not immediately respond to a request for comment Thursday on whether the South Carolina Republican would now attend the speech.

Reid spokesman Adam Jentleson took aim at Vitter’s remarks, calling it “a sad commentary on the state of the Republican Party when a Republican senator is whining about having to show a modicum of respect to the President of the United States, and do the job his constituents hired him – and are paying him – to do.”

“We have a packed schedule this fall as Congress works to create jobs and get our economy back on track,” Jentleson said. “The American people are sacrificing every day as they try to make ends meet in this tough economy – it’s not too much to ask Senator Vitter to sacrifice a few hours on his couch to vote on a bill that will create jobs and spur small-business entrepreneurship by streamlining our patent system. I’m sure he’s aware that there are televisions in the Capitol as well.”

Ahead of Obama’s jobs speech, the Senate is expected to hold votes Thursday afternoon on amendments to and passage of a patent reform bill.