“A lot of people never thought he would win the nomination, and a lot of people thought he would not win the presidency,” Mr. Nunes said. “And a lot of these people are not in a position to be in the next administration, and that’s refreshing.”

William Inboden, who worked at the National Security Council for President George W. Bush and was one of 50 people to sign the August letter, said he would not completely rule out working in a Trump administration.

“Any patriotic American who is asked to serve our country should be willing to do so and should give serious consideration to whatever position is offered,” said Mr. Inboden, who is now a professor at the University of Texas.

At the same time, he said, “the Trump team will have to decide how magnanimous they want to be toward the dissenters.”