Salt Lake City Mayor Ralph Becker said he personally urged Obama to visit the state during a meeting at the White House earlier this year, though he paused when describing how the president responded.
"He was ... gracious," Becker said.
It's highly unlikely that Obama will travel to Utah before the November election as he focuses on competitive states like Ohio, Florida and Colorado. And Utah is about as far from competitive as a state can get.
A Gallup poll released last week showed that Obama had a 26 percent approval rating in Utah, a state where Republican candidate Mitt Romney is generally beloved, in part because of his Mormon faith.
Rep. Jason Chaffetz, R-Utah, may be a campaign surrogate for Romney but said he would welcome a visit from Obama, noting that the president referenced Intermountain Healthcare in his first joint address to Congress and may benefit from visiting its hospitals.
"President Obama is perpetually in campaign mode, so if he doesn't see any prospect of winning he's not going to stop by," Chaffetz said. "I remember him famously saying we are not red states or blue states we are the United States of America. But we are a flyover state for this president. It's too bad."
If the president were to visit the state, Chaffetz said: "I would show up at the airport, but I'm not sure Jim Matheson would."
Matheson, a Democrat who has won six terms in the House, is locked in a tough re-election battle with Saratoga Springs Mayor Mia Love, who often ties herself to Romney and links Matheson to Obama.
Matheson has often voted against the president's legislative priorities, including health reform and an energy bill, though he did support the economic stimulus act passed shortly after Obama came into office.
"Jim Matheson is clearly trying to distance himself from Barack Obama," said Utah State University political scientist Damon Cann. "That being the case, the best thing Barack Obama can do for Jim Matheson is stay as far away from him as he possibly can."
Respect for the office • Matheson says he can't remember the last time he met with Obama personally, but would welcome him to visit Utah.
"When you are one of the smaller population states in particular, I think it is important for the president to visit," he said. "I think it is always helpful for whoever the president is to understand a Utah point of view on things."
And despite Chaffetz's jab, Matheson insists he would greet this president or any other who visits the state.
"Our whole delegation, including myself, greeted George Bush when he came to Utah," Matheson said. "That is the respect for the office that we show in our state."
President George W. Bush came to Utah four times while in office, including to mark the opening of the 2002 Winter Olympics and to raise money for Republican presidential candidate John McCain.
In one memorable visit in 2005, Bush's entourage drove from the airport to the Salt Palace where he would address the Veterans of Foreign Wars convention, and just as Sen. Orrin Hatch finished telling him how popular he was in the state, they were confronted by a group of anti-war protesters extending their middle fingers.
An angry Hatch later told KSL-TV: "You're always going to have nutcakes out there, no matter what you do."
President Bill Clinton had no similar encounters, in part because his two trips to Utah as president were exclusively ski trips to Park City where he celebrated his daughter's 18th and 19th birthdays.
The last sitting president who failed to visit Utah was Calvin Coolidge, who served in the 1920s, though President Dwight Eisenhower only took a few steps into the state during a quick stop at the Four Corners area, according to author Ron Fox, who along with West Valley City Mayor Mike Winder wrote a book on presidential visits to Utah called When the White House Comes to Zion.
Candidate Obama • Obama has been to the state, with his last visit coming in August 2007, while he was running for office. He held a private fundraiser in Park City and planned to shake a few hands before heading to the airport, but a large crowd of spectators gathered. He held an impromptu rally.
"This was supposed to be a 15-minute stop with about 20 people," said Obama, who spoke for about 20 minutes. "Somehow this grew a little bit."
Since then, first lady Michelle Obama has held a 2011 fundraiser in Park City and Vice President Joe Biden and his wife, Jill, came to the state in mid-July, where Biden took a shot at Romney.
"These guys have a social policy out of the '50s," Biden said at a fundraiser in the home of John and Kristi Cumming.
The Cummings were Democratic delegates in 2008, but they also contributed $4,600 to Romney, a personal friend, in an illustration of how deep Romney's ties are in the state.
The Republican candidate once owned a home in the state, attended Brigham Young University and later returned to lead the Olympics.
He visited the state in June for an exclusive weekend retreat in Deer Valley for his top donors. He brought in a number of top-line Republicans for the multiple-day strategy session, including Condoleezza Rice, Karl Rove, Paul Ryan and former Utah Gov. Mike Leavitt.
Cann, the Utah State political scientist, has advised a graduate student who studied presidential visits and notes that presidents tend to gravitate to states where they have support and spend less time in those that are "ideologically hostile."
They also steer schedules to spend more of their time in states that could make a difference in the election.
Presidential preferences • Outside of the Washington, D.C., metro area, Obama has held the most events in liberal-leaning New York, followed by his birth state of Hawaii, where he has vacationed in the summer, according to The Washington Post's POTUS Tracker, which has cataloged every presidential visit Obama has taken from January 2009 to June 2012.
The seven states he has yet to visit are Utah, Idaho, North Dakota, South Dakota, Nebraska, Arkansas and South Carolina. Cann said Obama's travel isn't out of step with past presidents like George W. Bush or Clinton.
"It is pretty rare for a president to make it to every single state in his first term," said Cann. "No one should read Obama having only made it to 43 states as a knock on the seven he hasn't visited."
Sen. Mike Lee, R-Utah, agrees.
"My instinct is to cut him some slack on that one," said Lee, who has cut Obama little slack on other issues. "Visiting 43 out of 50 states in three and a half years is pretty good. I'm sure he'll visit the others at some point."