The Senate voted Tuesday to limit debate on the New Strategic Arms Reduction Treaty (START), paving the way for final ratification of the arms-control pact as key Republicans defied their party leadership and announced support for the accord.

The move to invoke cloture passed by a 67-28 vote after several days of debate and unsuccessful Republican attempts to add amendments to the U.S.-Russia arms agreement.

The Senate could take a final vote to formally ratify the treaty as early as Wednesday.

Democrats need the votes of nine Republicans to reach a two-thirds majority of 67 to ratify the agreement, if all Democrats vote in favor.

Still, it appears the treaty will garner significantly fewer votes than past arms-control treaties that were approved by the Senate with large, bipartisan majorities of 90 votes for more.

“Today’s bipartisan vote clears a significant hurdle in the Senate,” said Sen. John Kerry, Massachusetts Democrat and chairman of the Senate Foreign Relations Committee. “We are on the brink of writing the next chapter in the 40-year history of wrestling with the threat of nuclear weapons. We’ve spent months building toward this moment.”

If the treaty passes, it will be a victory for the White House in a year of political setbacks. President Obama has made passage of New START during the postelection lame-duck session of Congress a top priority, even though he also needed to negotiate a deal on the budget and tax-cut extensions.

Mr. Obama also made the treaty, which limits Russian and U.S. strategic nuclear arsenals to 1,550 warheads for each side, a central focus of U.S. efforts to reset relations with Russia.

Additionally, the White House has said the treaty is important for Mr. Obama’s program to curb the spread of nuclear arms as part of a plan to ultimately rid the world completely of nuclear weapons. Further arms talks are planned for limits on tactical or battlefield nuclear missiles, limits on the production of fissile material, and cooperation on missile defenses.

Republican critics said the limits of New START are not verifiable because the treaty permits fewer on-site inspections than the arms treaty it replaces and because the 1,550 limit on warheads cannot be detected using satellites.

The Obama administration refused requests by senators to release the secret negotiating record with the Russians, fueling speculation that negotiators had made unwritten concessions to Moscow.

Despite Republican concerns on verification, Democrats appear to have lined up enough votes for passage. Over the past three days, more than nine Republican senators announced that they would vote to ratify the treaty. They include both Republican senators from Maine, Sens. Olympia J. Snowe and Susan Collins; both Republican senators from Tennessee, Sens. Bob Corker and Lamar Alexander; and Sen. Scott Brown of Massachusetts.

Other Republicans who have said they will vote for the treaty are Sens. George V. Voinovich of Ohio, Johnny Isakson of Georgia, Robert F. Bennett of Utah and Richard G. Lugar of Indiana, the ranking member of his party on the Senate Foreign Relations Committee.

Mr. Voinovich and Mr. Bennett will be leaving the Senate at the end of the 111th Congress.

Republican opposition to New START faltered after Monday’s closed session of the Senate on the treaty. As senators left that session, in which classified intelligence assessments were reviewed, the first wave of Republican defectors announced support for the treaty.

The Senate minority leader, Sen. Mitch McConnell, Kentucky Republican, and the minority whip, Sen. Jon Kyl, Arizona Republican, announced over the weekend that they would oppose ratification.

Mr. Kyl, who was leading the debate for Republicans on START, voiced particular concerns Tuesday that there was not enough time during the lame-duck session to fully debate the treaty.

“All of these interruptions and the season have resulted in a situation in which very few members are paying much attention, very few are on the floor really thinking about this, and, frankly, the other side does not have an open mind about accepting anything,” Mr. Kyl said.

He offered earlier this month to take up the START debate at the end of January with an eye to a vote on Feb. 5. Senate Majority Leader Harry Reid, Nevada Democrat, rejected the offer.

Mr. Kyl until this past weekend would not say how he planned to vote on the treaty. Instead, he worked with the Obama administration to win support for a 10-year, $85 billion plan to upgrade the aging U.S. strategic nuclear arsenal and the labs that maintain them.

The administration also made commitments in recent days that the treaty would not constrain U.S. plans to develop a European-based “phased adaptive approach” to missile defense for the United States and Europe. In a letter shared with Senate leaders, Mr. Obama pledged to “take every action available to me to support the deployment of all four phases” of U.S. missile-defense plans.

The letter from Mr. Obama, however, was not enough for Mr. Kyl, who said he wanted a commitment from Russia’s leaders that they would not try to withdraw from the treaty if the United States moved forward with the missile-defense plans.

Russia’s government has made a unilateral statement outside the formal treaty that it will pull out of the accord if U.S. missile defenses expand.

“Beyond what the Republicans explicitly got, the administration is going to have difficulty in the next Congress doing anything without the Republicans,” said Henry Sokolski, executive director of the Nonproliferation Policy Education Center.

“That empowers the Republicans, if they choose, to add to the president’s agenda proliferation and strategic restraint initiatives of their own. I don’t know if they will do it, but it puts them in a position to do it. That is the silver lining.”

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