Each year in May, Congress, the president, and most state governors proclaim a National Day of Prayer, inviting Americans of all faiths to pray. But Dobson's wife, Shirley, heads a National Day of Prayer Task Force that mounts its own events nationally — including at the Capitol — which are "specifically limited to the Judeo-Christian heritage." Michael R. Otterson, media relations director for The Church of Jesus Christ of Latter-day Saints, said that despite an outpouring of angry e-mails from members, "We don't consider it an issue." Mormons, he noted, can sponsor their own events.

Scholars say Protestant evangelicals who form the base of the Republican Party have more profound theological conflicts with the LDS Church. (Despite his efforts to improve the dialogue between LDS Church members and Protestant evangelicals, Johnson said he doesn't believe LDS beliefs are a "Christian doctrine.")

Chief among those is the LDS Church's assertion that early Christian leaders fell away from God's truth and that it took Smith's discovery of the Book of Mormon — a historical account that asserts ancient Hebrew tribes landed here and became the ancestors of Native Americans — to "restore" true Christianity."

"One of the first things that puts off traditional Christians is the idea of a restoration (of Christianity) being required," said Millet. "Catholics and Protestants would believe in a continuation of Christianity without a break."

But "there's a new breed of evangelical who is at least willing to put Mormonism on the table," Millet said.