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A top Democrat predicted Monday that the Senate will approve a new arms control treaty with Russia, but conceded that it will take "house by house combat" to collect enough votes from recalcitrant Republicans to prevail.

The comments by Sen. Charles Schumer, D-N.Y., came a day after Senate Minority Leader Mitch McConnell, R-Ky., said he would oppose the accord, complicating President Barack Obama's prospects for achieving his top foreign policy priority.

Schumer said Democrats have now picked up the support of GOP Sen. Thad Cochran Mississippi, and said he thinks Democrats will get the 67 votes the Constitution requires to ratify a treaty. He said Democrats will need nine or 10 Republican votes to prevail.

"It's going to be a real slog, house by house combat if you will," Schumer told ABC's "Good Morning America." ''But I think we'll be there."

On Sunday, McConnell criticized the treaty's verification system and expressed concern that the pact would limit U.S. missile defense options even though Obama insisted Saturday that the treaty imposes no restrictions on the system aimed at protecting the United States and its allies from ballistic missile attacks.

Undeterred by McConnell's opposition, Majority Leader Harry Reid, D-Nev., announced Sunday night that the Senate would vote Tuesday to end debate on the treaty 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 the 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."

A sixth day of debate was scheduled for Monday that included a closed session to discuss intelligence issues.

The White House and Democrats are determined to win approval of the treaty before January, when Republicans increase their numbers in the Senate, dimming its outlook. During a rare Sunday session of the Senate, Democrats turned back a GOP amendment to change the treaty, which would have effectively killed it.

Just weeks after Obama's self-described "shellacking" in the Nov. 2 midterm elections, ratification of the treaty would cap a string of political victories for the White House. Congress endorsed the president's tax compromise with Republicans and voted Saturday to repeal the military's ban on openly gay servicemembers.

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 landmark 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.

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.

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.

After several hours of debate Sunday, the Senate voted 60-32 to reject a measure to add language on tactical nuclear weapons to the treaty's preamble, which would have forced it back to negotiations, dooming the accord. Republicans Bennett, Lugar and Tennessee's Bob Corker and Lamar Alexander voted with the Democrats. It marked the second time in two days that Democrats had stopped GOP amendments.