A chief proponent of repealing the military's ban on openly gay service members wants the Senate to take up his top priority before dealing with a key nuclear-arms reduction treaty.

Sen. Joe Lieberman (I-Conn.) expressed hope that a bill that nixes "Don't ask, don't tell," which passed the House on Wednesday, will be taken up immediately following completion of the omnibus appropriations bill that funds the government.

"I hope it could come up Sunday or Monday of next week. And I really believe that, after the tax cuts have been passed, which they have been in the Senate, the spending bills for the government are approved, this is the next most important and urgent thing to do," Lieberman told CNN.

Congressional leaders have to juggle a number of legislative items before lawmakers leave for the Christmas holiday. But Lieberman said repealing "Don't ask, don't tell" is unlikely to get done with Republicans in control of the House.

"Let me just talk straight, hard political reality. If we don't repeal 'Don't ask, don't tell' in this 111th session of Congress, the new Congress, I'm afraid, is not going to repeal it, and then we will have to depend on the courts to repeal it," he said. 

The Senate, with strong support, moved to debate the Strategic Arms Reduction Treaty (START) on Wednesday, advancing one step closer to a ratification vote. President Obama has called both "Don't ask" repeal and START top priorities.

Senate Majority Leader Harry ReidHarry Mason ReidTo end sugar subsidies, conservatives can't launch a frontal attack House presses Senate GOP on filibuster reform A pro-science approach to Yucca Mountain appropriations MORE (D-Nev.) has pledged to keep lawmakers in Washington through the weekend and into next week — and maybe even after Christmas — to complete unfinished business. But Senate Republicans look like they could put up a fight on the appropriations bill, which could delay consideration of the "Don't ask, don't tell" repeal.

But Lieberman noted that the House passed its repeal bill with a special order, meaning that Reid could take it up sooner than expected. The Connecticut senator again expressed confidence that repeal has 60 votes, especially with newfound support from Sen. Olympia Snowe (R-Maine).

"Well, look, there may be a battle there, but we have got 61 votes. I have been saying this. People thought I was puffing, but I knew I had those votes, and I know I have got at least one more Republican who will come with me," he said. "I — I think we're — we're going to — we're going to make it happen before we leave."