The issue, however, has been raised on those occasions when Mormons have sought the Oval Office: George Romney was asked about it during his bid in 1968, Sen. Orrin Hatch discussed it when he ran in 2000, and now Mitt Romney.
"It is being raised," says Phil Barlow, a professor of Mormon history and culture at Utah State University. "I've heard it a bit lately."
Romney says he doesn't believe in the supposed prophecy, nor did his father when he ran.
"I haven't heard my name associated with it or anything of that nature," Mitt Romney told The Salt Lake Tribune during an interview earlier this year. "That's not official church doctrine. There are a lot of things that are speculation and discussion by church members and even church leaders that aren't official church doctrine. I don't put that at the heart of my religious belief."
The disputed prophecy was recorded in a diary entry of a Mormon who had heard the tale from two men who were with Joseph Smith in Nauvoo, Ill. when he supposedly declared the prophecy.
"You will see the Constitution of the United States almost destroyed," the diary entry quotes Smith as saying. "It will hang like a thread as fine as a silk fiber."
Not only will the Mormons save the Constitution, under the prediction, but the prophecy goes further, insinuating that Mormons will control the government.
"Power will be given to the White Horse to rebuke the nations afar off, and you obey it, for the laws go forth from Zion," the prophecy says.
The LDS Church denounces the premonition, which was recorded 10 years after Smith's death. A church spokesman pointed to a quote from the faith's sixth president, Joseph F. Smith, who called the prophecy "ridiculous."
"It is simply false; that is all there is to it," the church prophet was quoted saying.
Joseph Smith, who Mormons believe found ancient gold plates and transcribed them into the Book of Mormon, ran for president in 1844, a year after he supposedly told of the White Horse Prophecy. Smith was murdered by a mob shortly thereafter.
So far, it hasn't been overtly discussed in reference to Romney's bid, but he told The Tribune previously that it was raised in the 1968 presidential run of his father, George Romney.
"It came up in the race, but he didn't believe in it," the younger Romney said in 1999.
In fact, George Romney said there are different interpretations of what Smith and Brigham Young, another Mormon prophet, were saying, according to a 1967 edition of Dialogue: A Journal of Mormon Thought:
"I have always felt that they meant that sometime the question of whether we are going to proceed on the basis of the Constitution would arise and at this point government leaders who were Mormons would be involved in answering that question," George Romney was quoted as saying.
In the 2000 presidential race, the prophecy again made news during Hatch's failed bid for the White House. The Utah Republican and Mormon commented on the Constitution hanging by a thread during a radio interview, fanning thoughts of whether he was referring to the prophecy. Hatch says he was not referencing the premonition.
Mitt Romney has faced a barrage of questions about his religion from the news media but few in public from voters. One man in New Hampshire last week told Romney he wouldn't vote for him because Romney's a Mormon. But the guy added that he was a liberal and voting for Hillary Clinton.
On the trail, Romney talks generally about his belief in God but does not engage in doctrinal debate over details of his faith. He declines often to go into the specific tenets of the Mormon religion, saying that he is not a spokesperson for his church.
Ann Marie Curling, a Mormon in Kentucky who backs Romney, knows of the prophecy but puts no stock in it.
"It's definitely not playing into why I support him," says Curling, who runs a pro-Romney blog.
She says the few who believe in the prophecy are in the "extreme" fringes of the faith. "I don't see it being the reason everyday LDS persons are supporting him."
While the LDS Church does not accept the White Horse Prophecy as doctrine, several former leaders of the faith have spoken of the threat to the Constitution at various times, according to research by George Cobabe, who studied the prophecy's origins for the Foundation for Apologetic Information & Research. The group's mission is to defend the church and correct misunderstandings.
He says the concept of religious people saving the Constitution in the last days is a common theme for many faiths, but adds the White Horse Prophecy is bunk.
"I don't think the White Horse Prophecy is fair to bring up at all," he says. "It's been rejected by every church leader that has talked about it. It has nothing to do with anything."
Barlow, the Utah State University professor, says probably 10 percent to 20 percent of Mormons in America have heard of the prophecy by name but that many more have likely heard bits and pieces of it.
"It's dubious whether this originated with Joseph Smith but it seems to have a life of its own," Barlow says. "While most Mormons may not have heard of it, there are some themes that have some currency."
The main theme is the apocalyptic end of the world and the phrase that the Constitution - which Mormons believe was divinely inspired - will "hang by a thread."
Still, Barlow says it's doubtful the so-called prophecy will make a big splash during the campaign.
"It's too esoteric than bigger things like polygamy that will get brought up," he says, referring to the practice of marrying multiple wives that the church officially denounced in 1890.
In the last days, the U.S. Constitution will "hang by a thread" and a Mormon will ride in on a metaphorical white horse to save it.
* Background: The story was hearsay - supposedly uttered by LDS Church founder Joseph Smith - recorded in a Mormon diary.
* Fact: LDS Church leaders have declared it is false.
* Reaction: Mitt Romney doesn't believe the legend.
"I don't think the White Horse Prophecy is fair to bring up at all. It's been rejected by every church leader that has talked about it. It has nothing to do with anything."
Studied the prophecy's origins for the Foundation for Apologetic
Information & Research