In South Carolina, tea-party activists are looking to mount a primary challenge against Mr. Graham, whom they oppose in part because he voted to confirm Mr. Obama’s Supreme Court nominees, Sonia Sotomayor and Elena Kagan…

Another potential target is Tennessee’s Mr. Alexander, whom tea-party activists see as too centrist, citing examples such as his vote last July against blocking an Environmental Protection Agency regulation on utilities.

“He is much too close to the Democrats,” said Katherine Hudgins, a tea-party activist from Murfreesboro, Tenn. “We believe he’s an environmentalist at heart. He’s gone to the dark side.”…

Others feel disillusioned with the movement itself. Allen Olson, founder of a tea-party group in Columbia, S.C., describes the movement’s members as “fractured” and “living in a bubble.”

Many are in denial about the demographic realities that powered Mr. Obama’s win, Mr. Olson said, and the movement has taken up a set of issues beyond its core mission. “It was supposed to be fiscal responsibility, and that was it,” Mr. Olson said. “They’ve branched out to things like immigration reform and voter-ID laws. Those are Republican issues, and I don’t think they should be tea-party issues.”