Polls in 1967 even showed him as the leader among rank-and-file Republicans. But on Aug. 31, 1967, he made a statement that most historians (and journalists at the time) say sunk his campaign, and it had nothing to do with being a Mormon.

When a radio interviewer questioned why he was changing his earlier strong support for the Vietnam War, he said, "When I came back from Vietnam (in November 1965), I'd just had the greatest brainwashing that anybody can get." He later decided he had been misled about the need for the war.

Among the media critics that attacked his new position that he had been "brainwashed" was Time magazine, which immediately declared that it was "so inept an explanation of his shifting views on Viet Nam that it could end his presidential ambitions." Many made fun of his use of the word "brainwashed" and quoted military officials saying they never brainwashed anyone. Others who traveled with Romney said they had not been brainwashed.

Romney withdrew from the race on Feb. 28, 1968. At the party's convention, he finished sixth, with 50 votes on the first ballot (44 from Michigan and six from Utah — showing fellow Mormons wished him well). Eventual winner Richard Nixon named Romney to his Cabinet as secretary of Housing and Urban Development.

• Morris (Mo) Udall, 1976. Udall was a well-respected Democratic congressman from Arizona, a former pro basketball player and a Mormon who had not been active in the LDS Church since his teenage years. The question of blacks and the LDS priesthood hurt him nevertheless.

Udall had narrowly finished in second place in a string of primaries in 1976. But he was gaining ground on Jimmy Carter in Michigan, which was seen as a chance for Udall to break through, finally win one, and maybe stop Carter's momentum.

But black Detroit Mayor Coleman Young, a Carter supporter, told a gathering of black Baptist ministers that while Carter had tried to open the front doors of the church to blacks, Udall's church "won't even let you in the back door."

Udall biographers Donald W. Carson and James W. Johnson wrote that Udall responded by saying that "he had split with the Mormon Church over its policies toward blacks 30 years earlier. Udall called for Young to apologize and for Carter to repudiate the accusation. Neither did."

Udall supporters also noted that Carter attended a church in Plains, Ga., that still barred blacks.

Udall lost the Michigan primary by three-tenths of a percentage point and Carter went on to ultimate victory.

Interestingly, Udall (who lost an eye as a child) would joke about his chances during the campaign by saying, "I'm a one-eyed Mormon Democrat from conservative Arizona. You can't find a higher handicap than that."