The challenge for reformist Republicans, however, is reconciling their new, softer tone with other members of the party still pushing for confrontation and radical policy changes. The party’s House and Senate leaders haven’t embraced the new message, and the one who came closest to doing so — House Majority Leader Eric Cantor (Va.) — lost his primary last month to a tea-party insurgent.

Republicans pushing for harsh action to deport tens of thousands of Central American children detained at the border could also undercut attempts at fashioning a more compassionate image for the party.

“There will be Republicans who will say we should be cutting these programs and they’re too big and Ryan’s not doing that,” said Ron Haskins, who worked on welfare issues for congressional Republicans and as an adviser to Bush. “It isn’t clear yet that the party will follow. It’s a huge risk.”

Liberals are deeply skeptical of the new GOP ideas, arguing that most are cynical attempts to soften the party’s brand without fundamentally changing its attitude toward helping the poor.