So why the persistent link between plural marriage and modern-day Mormonism?
It may simply be a problem of branding, said Kathleen Flake, who teaches American religious history at Vanderbilt University in Nashville.
"Mormonism's 19th-century brand was polygamy, and no other attribute has had the power to replace it," Flake wrote in an email. "In similar fashion, some still think of it as 'the American Church,' even though today the majority of its members live outside the United States. Even in the 19th century, however, polygamy was the catch-all for a variety of things about Mormonism that Americans, religious and otherwise, did not like: new scripture, prophets, priesthood government, for example. Mormons were and apparently still are believed to be just too different. Not surprisingly, when asked to identify Mormon difference the old catch-all brand comes up."
Michael Otterson, public-affairs director for the LDS Church, was not surprised about the polygamy response, but senses the perception is changing and believes it eventually will fade away.
"We feel we are making really good headway on the polygamy issue," Otterson told The Tribune. "We've all got institutional memories where journalists [and headline writers] would frequently make reference to 'Mormon polygamists' when talking about the FLDS [Fundamentalist Church of Jesus Christ of Latter-Day Saints]."
In the past few months, that is happening less and less, he said. "We've talked to a lot of journalists and the polygamy issue never came up."
The problem these days, Otterson said, is with the general public and popular culture.
"If you've watched a string of episodes of [HBO's] 'Big Love' or [TLC's] 'Sister Wives,' you are going to have a negative perception of polygamy," he said. "It is not possible to watch one of those series and feel good about it."
Responses from some poll participants revealed that Americans' concerns extend beyond confusion between the LDS Church and polygamy-practicing offshoots. Some knew the difference, but worried that the practice remains part of Mormon history and, to some extent, its doctrine.
In time, Otterson said, Mormonism's more favorable aspects will replace polygamy to outsiders. That's why the LDS Church launched the "I'm a Mormon" campaign to provide the public with a more well-rounded view of the faith and its followers.
The advertising effort has been "very successful," Otterson said. "People identify with it and are refreshed by it. It seems to be addressing the [Mormon] stereotype issue."
The Tribune poll may support the wisdom of the church's ad campaign.
Of the 42 percent of respondents who reported knowing a "great deal" or at least something about Mormonism, half said they knew a church member personally.
Of those who felt very or somewhat comfortable with the prospect of a Mormon commander in chief, 21 percent cited the LDS Church as being "pro-family" for their positive impression, followed by 19 percent who called members "friendly."
"That is consistent with what we've seen," Otterson said. "When you know a Latter-day Saint, not only are you likely to know more about the church, but also to feel better about it."
But it can't be just a casual acquaintance, said David Campbell, professor of political science at Notre Dame and co-author of American Grace: How Religion Unites and Divides Us.
"If you only know a Mormon in passing, you might be aware that they are different," Campbell said. "But if that's all you know, that's probably going to make you uneasy. It's not until you make a deep relationship that all those things that initially seemed strange fade away."
The "I'm a Mormon" campaign or similar efforts may do a little good, said Campbell, a Mormon, but they "breed a sense of complacency that church public affairs is handling this."
Americans will not embrace a more positive view, he said, "until Mormons themselves build bridges to neighbors of other faiths, and that will not happen until the church leaders make that a priority."
As long as the church puts high time demands on its members, they will mostly associate with other Mormons. It's not a question of antagonism, he said, "just that people like to be around others like themselves."
Ultimately, the polygamy link to Mormonism won't go away, either, said Valerie Hudson, a political-science professor at Brigham Young University, until Mormons themselves stop believing that it is the marriage pattern in heaven.
Regular Americans "rightly suspect that there are a decent amount of Mormons about 50 percent who believe they will be practicing polygamy again someday," Hudson said, "if not here, at least in the hereafter."
One poll respondent, Alice Ross, of Butler, Pa., said she doesn't like the LDS teaching that people can have more than one spouse in the afterlife.
"They don't practice it today," Ross said, "but marriage can determine where they have space in heaven."
Hudson argues that plural marriage, as described in Mormon scriptures, was an exception to the rule of monogamy, much as God asking Abraham to sacrifice his son Isaac was not a mandate for all.
"Just as the [LDS] Church would not be in favor of legalizing child sacrifice, the church is not going to be in favor in legalizing polygamy," she said. "There is doctrinal confusion on this issue among a majority of Mormons. … It will continue to be a source of concern not only within the LDS community but within the broader American community as well."
Salt Lake Tribune reporter Matt Canham contributed to this report.