While the showdown vote was set for Friday morning, just after 3 p.m. on Thursday Mr. Reid came to the Senate floor to move that it be called instead at 4:15. That forced senators like John McCain of Arizona and Lindsey Graham of South Carolina, members of the Senate Armed Services Committee who have said that they find the act of filibustering a defense secretary distasteful, to cast votes that had the same result as a filibuster, even if they refused to call it that.

Four Republicans joined Democrats in voting that debate on the nomination should end: Senators Thad Cochran of Mississippi, Susan Collins of Maine, Mike Johanns of Nebraska and Lisa Murkowski of Alaska. Senator Orrin G. Hatch of Utah voted present because he said he was wary of the precedent a no vote would set, even though anything other than a yes vote had the same practical effect on the outcome.

Because of parliamentary rules, Mr. Reid voted with Republicans to allow him to bring the Hagel nomination back for another vote. Counting Mr. Reid, Mr. Hagel was actually just one vote shy of the 60 needed.

Given the outcome, a major matter of concern for the White House over the next 10 days is that Mr. Hagel’s opponents — an array of groups that includes conservative and pro-Israel forces — could intensify their campaigns to defeat his nomination.

Leaders of these groups said in interviews that they expected their efforts to include more phone calls urging conservative voters to tell their senators to vote no; new efforts to unearth embarrassing details from Mr. Hagel’s past; and, potentially, a new round of television advertisements pressuring Democrats to drop their support for him.

“My intention is to keep doing what we’re doing, but only to escalate the effort,” said David Brog, the executive director of the large, pro-Israel evangelical group Christians United for Israel.

Republicans were moving on other fronts to block Mr. Obama as he tries to put together his national security team. Senator Rand Paul of Kentucky has said he will place a hold on the nomination of the president’s director of central intelligence, John O. Brennan, and Mr. McCain and Mr. Graham also said they intended to use Mr. Brennan’s nomination to force the administration to answer questions about the September attack in Benghazi, Libya. “It’s a time-honored practice,” Mr. McCain said. “It’s a way for us to get information.”