“Before the Gang of Eight and the immigration debate, I think many conservatives as well as some establishment Republican folks saw Senator Rubio as a possible bridge candidate between the conservative Tea Party base of the G.O.P. and more establishment G.O.P. voters,” said Greg Mueller, a conservative public relations executive who opposed the Senate bill. “That position is on much shakier ground today because conservatives and the Tea Party see the immigration bill as a big-government piece of legislation resembling Obamacare.”

Republicans strongly opposed to the immigration bill said they had little sympathy for Mr. Rubio.

“I don’t think we’re doing any damage to him,” said Representative Tim Huelskamp, Republican of Kansas. “I think he’s done damage to himself with the amnesty bill.”

Alex Conant, Mr. Rubio’s spokesman, said: “Immigration is a personal issue for Senator Rubio, and he took it on because he thought it was the right thing to do. There may be some political implications, especially in the short term, but it wasn’t an issue he believed he could ignore. We don’t expect any parades for our work on this.”