Even if these efforts serve only to inconvenience the White House and cause the president and his nominees some mild political damage, Republicans say they are satisfied that they are forcing the confirmation process to be more deliberative.

“Probably the best-known power of the United States Senate is advise and consent,” said Senator Lamar Alexander, Republican of Tennessee. “Movies have been made about it, books have been written about it. It’s what we do. And we’d be derelict in our duty if we didn’t examine the qualification of our president’s cabinet.”

But Democrats said the process, particularly with Mr. Hagel, had hardly been reflective, let alone worthy of the Senate.

Senator Barbara Mikulski, Democrat of Maryland, allowed that her Republican colleagues were entitled to ask questions. “But I understand that Jack Lew had 638 questions that he had to answer from one senator,” she said. “Now, really? If you don’t want the guy or gal, vote against them. But don’t drag it out. That’s not politics, that’s petulance.”

Republicans in the Senate, joined by an array of conservative activists, waged an all-out campaign to discredit Mr. Hagel, digging into his financial records for evidence that he was paid by anti-American groups and scouring his old speeches for signs that he was hostile to Israel. Those efforts produced little, forcing Republicans to acquiesce after filibustering his nomination in an initial vote this month.

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 sequestration set to go into effect — cuts that will fall hard on the Defense Department if Congress cannot negotiate a compromise — Mr. Hagel will inherit myriad challenges.