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More than a dozen Republicans joined Senate Democrats on the 71-to-27 vote to cut off the debate. Republicans who opposed Mr. Hagel, a former Republican senator from Nebraska, had insisted that they needed more time to examine his record.

The Senate scheduled a vote on the nomination for Tuesday afternoon. Mr. Hagel requires a simple majority of 51 to be confirmed.

Democrats said that Mr. Hagel was a strong pick for the job, considering his background in public office and as a soldier in the Vietnam War. They said that the Senate needed to clear Mr. Hagel's nomination so he could get to work at the Pentagon, given national security issues around the world and pending budget cuts at home.

Republicans said they believed that a shaky performance by Mr. Hagel at his confirmation hearing and his past statements on Israel and a variety of other issues had disqualified him.

John Cornyn, the No. 2 Senate Republican, said Mr. Hagel's worldview was "dangerously misguided," and he warned that the nominee was ill prepared to handle such a major post. "I don't think we want a secretary of defense that has to learn on the job," he added.

But Senator Harry Reid, the majority leader, accused Republicans of stalling the nomination earlier this month for political gain.

"What has their filibuster gained? Twelve days later, nothing has changed," he said. "Senate Republicans have delayed for the better part of two weeks for one reason and one reason only: partisanship."

The action in the Senate on Tuesday will help bring to a close one of the most unusually contentious cabinet-level nomination fights in years, a clash that surprised many in Washington for how personal and bitter it became considering that Mr. Hagel, a Republican senator for two terms, worked alongside many of his antagonists until just four years ago.

But even before Mr. Hagel takes office, questions are growing about whether the fight will wound his ability to lead the Pentagon at a time of upheaval both at home and overseas. With a series of huge budget cuts known as the sequester set to go into effect at the end of the week — cuts that will fall hard on the Defense Department if Congress cannot negotiate a compromise — Mr. Hagel will inherit myriad challenges.

Further, the tension between the White House and Republicans on Capitol Hill will not end with Mr. Hagel's confirmation. Republicans have already trained their sights on the next nominee they see as vulnerable: John O. Brennan, who is President Obama's pick to become director of the Central Intelligence Agency.

Senator John McCain of Arizona and Senator Lindsey Graham of South Carolina have threatened to hold up Mr. Brennan's nomination over questions about the attack last year on the American diplomatic mission in Benghazi, Libya. Both men made similar demands of Mr. Hagel, who, unlike Mr. Brennan, has had no role in formulating the Obama administration's defense and national security policies.

Senator Rand Paul of Kentucky has asked Mr. Brennan to answer questions about a topic that has been thrust to the forefront of the debate over national security: the government's use of drones.

But even if a handful of vocal Republicans succeed in temporarily blocking Mr. Brennan, they face the reality that they are unlikely to be able to hold up his nomination indefinitely.

The Hagel vote came as the Finance Committee agreed by a margin of 19 to 5 that the Senate should confirm Mr. Obama's nominee for Treasury secretary, Jack Lew, suggesting that the president's cabinet picks were moving ahead.