Senate Republicans reacted with alarm and dismay to President-elect Donald J. Trump’s decision to nominate Representative Matt Gaetz, Republican of Florida, for attorney general, and several said they were skeptical that he would be able to secure enough votes for confirmation.

“He’s got his work really cut out for him,” Senator Joni Ernst, Republican of Iowa, said, chuckling as she spoke.

Senator John Cornyn, Republican of Texas, raised his eyebrows when reporters informed him of Mr. Trump’s choice.

“I’m still trying to absorb all this,” he said, adding: “I don’t really know him, other than his public persona.”

Mr. Gaetz, who has been one of Mr. Trump’s fiercest attack dogs on Capitol Hill, has routinely used his position on the House Judiciary Committee to question the motives of Justice Department officials and rail against what he has called the “deep state.” He was also investigated by the Justice Department for child sex trafficking, though Mr. Gaetz was never charged with any crimes.

But Mr. Gaetz, who was just re-elected to a fifth term, remains under ethics investigation for his conduct, which includes allegations of sexual misconduct and illicit drug use; sharing inappropriate images or videos on the House floor; misusing state identification records; converting campaign funds to personal use; and accepting impermissible gifts under House rules. Mr. Gaetz has denied the allegations as political payback and said they are built on lies.