Washington (CNN) -- The Senate on Thursday rejected a Democratic bid to open debate on repealing the "don't ask, don't tell" policy banning openly gay and lesbian soldiers from military service, possibly killing any chance for it to get passed in the current congressional session.

However, a bipartisan group of senators immediately said they would raise the issue again in a separate piece of legislation. It was unclear if the bid to separate the repeal provision from a larger defense authorization bill would increase its chances for approval.

Senate Majority Leader Harry Reid, D-Nevada, called Thursday's vote without an agreement with any Republican senators to support the motion, ensuring it would fail. The vote was 57-40 in favor of the cloture motion that required 60 votes to pass.

A Republican filibuster forced Democrats to seek a deal that would get them the necessary GOP support to get the 60 votes to proceed. The Democratic caucus has 58 members, meaning they needed at least two Republicans to join them to overcome the filibuster.

Reid had been negotiating with moderate Republican Sen. Susan Collins of Maine for her support, and he postponed a planned vote Wednesday to allow more time for the talks to reach agreement.

However, Reid announced Thursday he was calling the vote to open debate on the defense authorization bill, saying it was time to act on it after months of Republican obstruction and intransigence.

Collins, apparently caught by surprise, missed the start of Reid's speech and requested a chance to question him on the Senate floor. She reiterated her support for repealing "don't ask, don't tell" and asked if the deal she had been discussing with Reid on Wednesday still stood.

Reid indicated he would honor parameters of the deal, which would allow Republicans to offer up to 10 amendments along with ample time for debate, but he refused to make an outright commitment. He blamed Republican leaders for the situation and praised Collins for being the only GOP senator he could even speak to about a possible deal for her support.

In response, Collins said, "I am perplexed and frustrated that this important bill is going to become a victim of politics. We should be able to do better."

The vote then proceeded, with Collins joining Democrats in voting to open debate while one Democrat, newly elected Sen. Joe Manchin of West Virginia, voted with the filibustering Republicans. Manchin's opposing vote killed any chance for the Democrats to succeed.

President Barack Obama said in a statement that he was "extremely disappointed that yet another filibuster has prevented the Senate from moving forward" with the defense authorization measure that includes the repeal provision.

Noting support for repeal from the defense secretary, the Joint Chiefs of Staff chairman and a majority of Americans, Obama said the "don't ask, don't tell" policy "weakens our national security, diminishes our military readiness, and violates fundamental American principles of fairness, integrity and equality," Obama's statement said.

"While today's vote was disappointing, it must not be the end of our efforts," Obama said. "I urge the Senate to revisit these important issues during the lame-duck session."

Gay rights advocacy groups, including those comprising military personnel, immediately condemned the Senate vote.

"Today leaders of both parties let down the U.S. military and the American people," said Joe Solmonese, president of the Human Rights Campaign. "Instead of doing what is right, 'the world's greatest deliberative body' devolved into shameful schoolyard spats that put petty partisan politics above the needs of our women and men in uniform."

Solmonese added. "This fight is too important to give up despite this setback and we will continue fighting in this lame-duck session. It's not over."

Sen. Joe Lieberman, an independent from Connecticut who caucuses with the Democrats, later said he believed that up to four Republican senators -- Collins, Scott Brown of Massachusetts, Lisa Murkowski of Alaska, and Richard Lugar of Indiana -- might support a separate repeal proposal that he will introduce with Collins and Sen. Mark Udall, D-Colorado.

Before Thursday's vote, Reid complained that all 42 of the GOP senators have pledged to block action on any measure before the chamber deals with extending Bush-era tax cuts and authorizing government spending for the rest of the fiscal year.

The Democratic strategy appeared to be to try to persuade Collins to vote for opening debate on the measure so that the two other Republicans who also have expressed support for a repeal -- Brown and Murkowski -- also might do so. Murkowski announced her support for a repeal in a statement Wednesday.

Democrats were pushing for action now because the new Congress in January brings a Republican-controlled House and a diminished Democratic majority in the Senate, which will make repealing "don't ask, don't tell" more difficult.

Collins said Wednesday she had asked Reid to delay the vote until after the Senate completes work on the package of tax measures negotiated by the White House and congressional leaders, which Republicans consider a top priority in the final weeks of the lame-duck session that ends in early January.

She also wanted Reid to schedule sufficient time to debate the defense authorization bill that contains the "don't ask, don't tell" repeal measure.

Both Reid and Collins, in their comments on the Senate floor Thursday, acknowledged an agreement for the debate to include up to 15 amendments -- 10 by Republicans and five by Democrats. However, Reid appeared to oppose the request to wait until the tax package had been passed.

Obama has been calling senators in both parties to urge their support, White House Press Secretary Robert Gibbs said. Before Thursday's vote, Gibbs told reporters that congressional repeal of "don't ask, don't tell" was the best way forward, and he believed it could happen before the end of the year.

Obama has called for repealing "don't ask, don't tell" after years of debate on the policy that detractors consider discriminatory. More than 400 military personnel were discharged under the policy in 2009, and a federal judge ruled it unconstitutional in a case that is under appeal.

Defense Secretary Robert Gates and Joint Chiefs of Staff Chairman Adm. Mike Mullen both have urged Congress to vote for a repeal. The measure before the Senate, which has already gained approval in the House, contains a process for implementing the change that requires certification from the president, the defense secretary and the Joint Chiefs chairman.

Gates has warned that court challenges to "don't ask, don't tell" could force an immediate repeal of the policy, rather than the process in the legislation that would allow the military to manage the change on a longer timetable.

CNN's Tom Cohen and CNN's senior congressional correspondent Dana Bash contributed to this report.