Rubio's approval rating with Tea Party backers is now at 47 percent, with 15 percent holding an unfavorable opinion of the Florida senator.

Those are still strong numbers, but mark a dip from the 52 percent support and 8 percent opposition Rubio had with Tea Party members when the group polled in February.

The senator's embrace of bipartisan compromise on the controversial issue appears to have taken a toll on his backing from the grassroots. House Republicans have balked at giving the Rubio-backed plan passed out of the Senate a vote in their chamber, and it has drawn sharp criticism from many of the party's conservatives.

Rubio's standing has also dipped in some key early-voting presidential primary states. He finished in fifth place in a recent Iowa presidential primary poll.