Some Republicans acknowledged how strange it felt to vote for Representative Thomas Kean Jr., who has not been seen for months. Mr. Kean issued a statement promising to be transparent about his situation.

The acting attorney general said the administration was preserving a broad order shielding the president and his family from audits of already filed returns, despite dropping a $1.8 billion payout fund.

Republicans hoped the acting attorney general’s vow that the administration was “not moving forward” with a fund for people claiming to be victimized by the government would unlock the votes.