Mr. Castellanos said Mr. Rubio needed to be wary of all his new friends. “His biggest challenge is not to get captured by either the G.O.P. or the Tea Party,” he said. “It is to remain Rubio.”

The senator-elect appears to understand that his work is just beginning. In his victory speech on Tuesday night, after the salsa band stopped playing and one of the speakers joked about his future run for president, Mr. Rubio asked the crowd to pray that he would stay true to his ideals. On Wednesday, he dismissed talk of a White House race.

“It’s flattering and it’s fleeting,” he said. “Politics is full of one-hit wonders, of people that stood in a room like this with a bunch of cameras, and no one hears from them anymore.”

He added, “It’s not going to get to my head.”