Senate Majority Leader Harry Reid on Thursday filed a motion for cloture on the defense authorization bill, meaning that the first showdown vote affecting the language to repeal Don’t Ask, Don’t Tell (DADT) will take place on Tuesday afternoon.

The majority will need 60 votes on Reid’s motion in order to proceed Tuesday with consideration of the annual defense spending bill—a bill which includes language that could lead to repeal of the law banning gays from the military.

Vice President Joe Biden said Wednesday that Democrats have 55 votes to support repeal, but he did not boast any certainty that they can get the 60 to break a filibuster.

Reid filed his motion for cloture after Republican leader Mitch McConnell indicated his party members would not give “unanimous consent” for the Senate to take up the defense bill. McConnell said this week he thinks the DADT repeal language is “controversial,” but he did not identify it as the reason Republicans are withholding unanimous consent. Instead, he identified several other matters proposed for inclusion—matters involving immigration and Senate rules.

If the Democrats fail to pass the cloture motion on Tuesday, Reid has the option of calling for reconsideration of that motion whenever he wants.

If the Senate passes the cloture motion, Reid and McConnell will then discuss when various amendments to the legislation might be considered. One amendment that has been mentioned as a likely amendment from Republicans is one to strip the DADT language from the bill. On other legislation this year, Republicans have attempted to pass amendments aimed at making the underlying bill objectionable to supporters.

It is not certain when any DADT-related amendments might come up in consideration of the overall bill.

Meanwhile, various LGBT-related groups are stepping up pressure for a vote. One group from Arizona, known as HERO, stood and held up placards at a Senate Armed Services Committee meeting Thursday, urging committee minority leader John McCain to end his opposition to repeal of DADT. McCain has been one of the more vocal opponents of the repeal in the Senate.