Last year, when House Speaker Kevin McCarthy selected him to lead a new committee tasked with investigating threats posed by the Chinese Communist Party, he was the youngest Republican wielding a panel chairman’s gavel.
Mr. Gallagher also caught the eye of Senate Republican recruiters, who attempted last year to convince him to run against Senator Tammy Baldwin, Democrat of Wisconsin. But Mr. Gallagher decided against that bid, announcing at the time that he would seek re-election to the House.
His standing in the G.O.P. appeared to have shifted earlier this week, however, after he became the third House Republican to refuse to back the impeachment effort against Mr. Mayorkas. The charges, of refusing to uphold the law and breaching the public trust, were widely dismissed by legal experts as not meeting the constitutional threshold of high crimes and misdemeanors.
The effort to impeach Mr. Mayorkas failed by just one vote.
“The proponents of impeachment failed to make the argument as to how his stunning incompetence meets the impeachment threshold,” Mr. Gallagher said in a statement this week defending his decision, arguing that impeaching Mr. Mayorkas would “set a dangerous new precedent that will be weaponized against future Republican administrations.”
The House is expected to try to impeach Mr. Mayorkas again next week, once Representative Steve Scalise of Louisiana, the House’s No. 2 Republican who has been absent while undergoing treatment for blood cancer, returns to Washington.