Sean Duffy, the new transportation secretary, is facing his first major crisis just hours after his swearing-in.

Duffy, a 53-year-old former Wisconsin congressman and reality TV star, was approved on a 77-22 vote in the Senate.

Mr. Duffy, a former congressman who had appeared on track to sail through with little opposition, overcame a last-minute swell of Democratic anger over the White House’s sweeping funding freeze.