Washington (CNN) -- Unable to secure needed Republican support, Senate Democrats decided Wednesday to postpone a planned make-or-break vote on starting debate on repealing the "don't ask, don't tell" policy that bars openly gay and lesbian soldiers from the military.

Jim Manley, the spokesman for Senate Majority Leader Harry Reid, D-Nevada, said the showdown vote was delayed while negotiations continue on gaining GOP support necessary to overcome a Republican filibuster. Earlier, Reid said he was talking to one moderate Republican, Sen. Susan Collins of Maine, to try to gain her support.

Collins later told reporters she asked Reid to delay the vote until after the Senate completes work on a 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 wants Reid to schedule sufficient time for the defense authorization bill that contains the "don't ask, don't tell" repeal measure. If that happens, Collins said, there was a chance that she and other Republicans would join Democrats in opening debate on the measure.

"I am encouraged that the Majority Leader decided to postpone the vote he had scheduled for tonight," Collins said in a statement issued later Wednesday. "I urged him to do this so that we could consider the tax legislation first, which I believe could be on the floor as early as tomorrow and completed quickly. At that point, I believe we could move immediately to the Defense Authorization bill under a fair agreement, and I would vote to do so."

A Democratic source involved in the negotiations between Reid and Collins said that the outcome of Wednesday's talks showed "we now have a meeting of the minds" on the process.

Meanwhile, President Barack Obama has been calling senators in both parties to urge their support, White House Press Secretary Robert Gibbs said.

"I think we are very, very close to seeing that repeal pass," Gibbs told reporters, adding: "The president is encouraging Democrats and Republicans to get behind that repeal."

The controversial 1993 policy is part of a broader defense authorization bill that normally passes with bipartisan support.

To open debate on the measure, Senate Democrats need 60 votes to defeat a Republican filibuster. Currently, the Senate Democratic caucus has 58 votes -- 56 Democrats and two independents -- though it was not clear if every one of them would support a repeal.

For example, newly elected West Virginia Sen. Joe Manchin, who is completing the term of the late Sen. Robert Byrd, told CNN he was uncertain how he would vote on the issue. Therefore, the Democrats may need more than two GOP senators to join them in voting to open debate.

However, most Senate Republicans oppose repealing "don't ask, don't tell." In addition, 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 -- Sen. Scott Brown of Massachusetts and Sen. Lisa Murkowski of Alaska -- also might do so. Murkowski announced her support for a repeal in a statement Wednesday.

Sen. Joe Lieberman of Connecticut, an independent who belongs to the Democratic caucus and has been involved in the negotiations with Reid and Collins, told CNN that he hoped Brown and Murkowski might also vote for opening debate on "don't ask, don't tell" if Collins does.

At the same time, Lieberman said he advised Reid that if he was unable to strike a deal for Collins' support, the majority leader should delay the vote scheduled for Wednesday or else face certain defeat.

Collins had indicated she would vote to allow consideration of a repeal if Reid guaranteed ample time for a full debate and sufficient Republican amendments. Murkowski, in her statement Wednesday supporting repeal, also called for a full floor debate on the defense authorization measure.

Reid said Wednesday he would assure Collins that the debate on the measure could include 15 amendments on the measure -- 10 for Republicans and five for Democrats -- along with extra time to debate some of the GOP amendments if necessary.

Collins said later that she was satisfied with Reid's offer of 15 amendments, but wanted him to double the time offered for debate.

"There are many people in my caucus who disagree with my position" on the repeal, Collins told reporters. "They deserve an opportunity to offer amendments to strike that position, to modify it, and also to address other important and controversial positions in the bill."

Aides to Reid said that with little time remaining in the lame-duck session and Christmas recess approaching, the vote would almost certainly be the last chance to consider the repeal of "don't ask, don't tell" this year.

Democrats are 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.

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, Ed Henry and Ted Barrett contributed to this story.