The leaders of evangelical and other socially conservative groups say they do not believe that Mr. Bush, the former governor of Florida — whom they already view as the preferred candidate of the Republican Party’s establishment — would fight for the issues they care most about: opposing same-sex marriage, holding the line on an immigration overhaul and rolling back abortion rights.

The efforts to coalesce behind an alternative candidate — in frequent calls, teleconferences and meetings involving a range of organizations, many of them with overlapping memberships — are premised on two articles of conservative faith: Republicans did not win the White House in the past two elections because their nominees were too moderate and failed to excite the party’s base. And a conservative alternative failed to win the nomination each time because voters did not unite behind a single champion in the primary fight.

This time, social conservatives vow, will be different. They plan to unify behind an anti-establishment candidate by summer or early fall, with the expectation that they will be able to overcome any fund-raising advantage of the Republican elite by exerting their own influence through right-wing talk radio and social media, and by mobilizing an army of like-minded small donors. “Conservatives smell blood in the water,” said Kellyanne Conway, a Republican pollster who has participated in the vetting. “They feel they’ve got the best shot to deny the establishment a place.”

Ms. Conway said the candidates seen as having potential to energize the party’s right wing would be invited to make their case before national groups of social conservatives in the coming weeks and months.