While many party leaders are taking a wait-and-see approach before choosing sides in the presidential primary, Republican advisers to House and Senate campaigns said they were not eager for Social Security to become a central theme in their races next year. Several Republicans have said they are waiting for a series of debates to play out before making a decision.

One month after declaring his bid for the Republican nomination, Mr. Perry has solidified an early edge in polls. But his popularity among activists has not been widely echoed by the party establishment, which is at odds with how races often unfold.

Representative Peter Roskam, Republican of Illinois, said the party’s nominee needed to connect with suburban voters — moderates and independents — if he or she wanted to defeat President Obama next year. Mr. Roskam said Mr. Perry, whose state includes many suburban communities, “knows how to do it,” but added that as a presidential candidate his comments about Social Security and other issues might not play well…

“What I think you are seeing is that it’s partially establishment versus Tea Party, there’s no question about that,” said Mr. Weber, who is now a Washington lobbyist. He added, “How concerned should we be? People I talk to are concerned.”