The White House and Democrats are determined to win approval of the landmark treaty before January, when Republicans increase their numbers in the Senate, dimming its outlook. During a rare Sunday debate, Democrats beat back a GOP amendment to change the treaty, which would have effectively killed it. Senate Majority Leader Harry Reid, D-Nev., set a vote for Tuesday to end the debate and move to a final vote.

“It is time to move forward on a treaty that will help reverse nuclear proliferation and make it harder for terrorists to get their hands on a nuclear weapon,” Reid said, adding that debate soon “will come down to a simple choice: you either want to keep nuclear weapons out of the hands of terrorists, or you don’t.”

Hours earlier, Minority Leader Mitch McConnell, R-Ky., dealt a blow to the administration’s hopes for strong bipartisan support, criticizing the treaty’s verification system and expressing concern that the pact would limit U.S. missile defense options even though Obama insisted Saturday that the treaty imposes no restrictions on missile defense.

“Rushing it right before Christmas strikes me as trying to jam us,” McConnell said on CNN’s “State of the Union.” ”I think that was not the best way to get the support of people like me.”

While McConnell’s opposition did not come as a surprise, it unnerved the treaty’s backers, who wondered how hard he would work to defeat the accord. Treaties require a two-thirds majority of those voting in the Senate, and Republican votes are critical to Obama’s success in getting the agreement.

Democrats expect to get 57 votes from their caucus, with Sen. Ron Wyden, D-Ore., absent next week due to cancer surgery. Four Republican senators — Richard Lugar of Indiana, Olympia Snowe and Susan Collins of Maine and George Voinovich of Ohio — have said they back the treaty.

While backers fretted over McConnell’s decision, several Republicans said Obama’s letter to congressional leaders Saturday vowing to move ahead on missile defense carried considerable sway.

“It takes care of me,” said Sen. Robert Bennett, R-Utah, who indicated he was leaning toward voting for the treaty. Snowe said it was “important for the president to be emphatic with respect to missile defense and modernization” of the remaining nuclear arsenal. Voinovich welcomed the statement.

Sen. John McCain of Arizona, Obama’s presidential rival in 2008, said he was still undecided.

Obama and Russian President Dmitry Medvedev signed the accord — it is known as New START — in April. It would limit each country’s strategic nuclear warheads to 1,550, down from the current ceiling of 2,200. It would also establish a system for monitoring and verification. U.S. weapons inspections ended a year ago with the expiration of a 1991 treaty.

Proponents of the treaty, including much of the military and foreign policy establishment, cite the renewed weapons inspections and say the pact would keep the two biggest nuclear powers on the path to reducing their arsenals. Opponents assert it would restrict missile defense and argue that it has insufficient procedures to verify Russia’s adherence.

Sens. Dick Durbin, D-Ill., the Democrats’ No. 2 leader in the Senate, and John Kerry, D-Mass., the chairman of the Foreign Relations Committee, said in news show appearances that they believe they have the votes to ratify the treaty.

Majority Leader Harry Reid, D-Nev., expressed disappointment with McConnell’s opposition, but he suggested in a statement that several Senate Republicans “share the belief that this treaty is too critical to our national security to delay, and I look forward to strong bipartisan support to pass this treaty before we end this session of Congress.”

White House spokesman Tommy Vietor said, “We respect Senator McConnell’s view, but we were not surprised by it, and certainly were not counting on his support to achieve Senate approval.”

After several hours of debate Sunday, the Senate voted 60-32 to reject a measure to add language on tactical nuclear weapons to the preamble of the treaty. Such a move would have forced it back to negotiations, dooming the accord. It marked the second time in two days that Democrats had stopped GOP amendments.

Four Republicans voted against the amendment — Bennett, Lugar and Tennessee’s Bob Corker and Lamar Alexander.

Sen. Jon Kyl of Arizona, the No. 2 Republican in the Senate who has been leading the opposition to the treaty, said it needs to be fixed. “And we are not going to have the time to do that in the bifurcated way or trifurcated way that we’re dealing with it here, with other issues being parachuted in all the time.”

While Kyl did not predict whether the treaty would be rejected or ratified, he said gaining the two-thirds vote would depend upon whether senators would be able to consider the amendments Republicans wanted to offer.

“I predicted a couple of weeks ago that we would not have time to do this adequately, and I think my prediction’s coming true,” he said.

Lugar, the top Republican on the Foreign Relations Committee and one who supports ratification, said more amendments to the treaty needed to be heard.

“Several Republicans will support it, and I join the chairman in believing that there are the votes there. The problem is really getting to that final vote,” Lugar said.

Durbin and Kyl spoke on “Fox News Sunday” while Kerry and Lugar appeared on ABC’s “This Week.”