It is still not clear where the remaining Democrat, Senator Joe Manchin of West Virginia, stands. But White House officials have said they are cautiously optimistic all three will support Mr. Dettelbach.

“I’ve been talking to a number of Democrats who say how favorably impressed they have been with him, how favorably toward him they feel, but they want to watch the hearings just to make sure,” said Senator Sherrod Brown, an Ohio Democrat and a friend of Mr. Dettelbach’s who has been speaking to colleagues on his behalf.

“I’m pretty certain we’re going to confirm him,” he added.

The A.T.F. — the federal agency charged with enforcing the nation’s gun laws — is chronically underfunded and hamstrung by laws that limit its regulatory authority and ability to share information. Mr. Dettelbach would be its first director actually confirmed by the Senate in seven years.

Mr. Biden’s aides took months to select Mr. Dettelbach, 57, whose confirmation they see as a smoother prospect than that of the brash and confrontational Mr. Chipman: He is upbeat, avoids bombast, and has been guided by administration officials and a Senate sponsor, all anxious to prevent another defeat.

Seven former A.T.F. directors have endorsed him, as have dozens of law enforcement officials around the country, along with the International Association of Chiefs of Police, the largest such organization in the country, and the Federal Law Enforcement Officers Association, the largest such organization representing federal agents, including A.T.F. employees.

Even so, he faces the narrowest of paths to confirmation.

Democrats felt nearly as sanguine about Mr. Chipman, a former A.T.F. agent who worked until recently for the gun control group led by former Representative Gabrielle Giffords, after securing preliminary commitments from almost all Democrats. Then, over the summer, the National Shooting Sports Foundation, a gun manufacturers’ trade group, began quietly deploying its state-level affiliates to peel away Democratic support.

By September 2021, Mr. King, an independent who caucuses with the Democrats, told the White House he planned to vote against Mr. Chipman based on Mr. Chipman’s pledge to aggressively crack down on gun dealers, in a state where hunting remains hugely popular. It scuttled his nomination.