Senate Majority Leader Harry Reid (D-Nev.) has committed the Senate to a showdown on campaign finance legislation aimed at undoing a controversial Supreme Court ruling, despite the fact that he does not have the votes to break a GOP filibuster.

Following the Senate’s rejection of a House version of the supplemental war spending bill late Thursday night and Reid’s inability to move a small-business bill, the Democratic leader abruptly decided to turn to the campaign finance bill. Reid filed a cloture on the bill Thursday night, and the vote will be held Tuesday.

The Supreme Court threw out much of the controls on corporate election spending in its Citizens United v. Federal Election Commission decision earlier this year.

Since then, Democrats have sought to pass legislation reversing some of its provisions. They fear that Republicans could have an electoral advantage as a result of the ruling and that corporations could have undue influence in elections.

Despite their best efforts, they have yet to muster enough support. Democratic Conference Vice Chairman Charles Schumer (N.Y.), the primary sponsor of the bill, has made concessions aimed at drawing the support of moderate Republicans such as Sens. Olympia Snowe and Susan Collins of Maine and Scott Brown of Massachusetts.

Those efforts have been unsuccessful so far, and Schumer has struggled to keep Democrats in line while the legislation has languished.

Sens. Dianne Feinstein (D-Calif.) and Frank Lautenberg (D-N.J.) have both repeatedly said they will oppose the bill, largely because of an exemption for the National Rifle Association that was inserted during House consideration.

Despite the bleak prospects for passing the bill anytime soon, Democratic aides said Reid is intent on forcing a fight, largely because he and other leaders see a political advantage in making Republicans defend a system that Democrats argue favors powerful interests.

“This is a good issue for us. Don’t be surprised if you see it more than once,” a senior Democratic aide said late Thursday night.