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A new poll shows that Republican presidential nominee Donald Trump continues to hold a 15-point advantage over Democrat Hillary Clinton in the state, even with the recent entry of Utah-born anti-Trump conservative Evan McMullin.

But the Clinton campaign says it's not giving up on Utah, even if winning the state — which hasn't voted for a Democratic candidate since Lyndon Johnson in 1964 — is an "uphill battle."

The campaign opened its Utah field office Tuesday evening in a ceremony that featured senior Clinton policy adviser Jake Sullivan.

"This is not just a kind of superfluous exercise," Sullivan told The Salt Lake Tribune. "There's no doubt it's a hard lift, but we are not writing Utah off and that's part of the reason I'm here."

The Trump campaign also has hired a Utah director and is opening an office of its own.

The survey, released Tuesday by Public Policy Polling, an independent polling firm, shows that Trump leads Clinton 39 percent to 24 percent. Libertarian candidate Gary Johnson receives 12 percent and McMullin checks in at 9 percent in the first test of his support in the state since the Provo-born, Brigham Young University graduate and former CIA operative entered the race.

"There's not much of a chance that Utah's actually going to go Democratic this year," Dean Debnam, president of Public Policy Polling, said in a statement. "But with Gary Johnson in double digits and Evan McMullin almost there, there is a pretty decent chance that Donald Trump will end up winning the state with less than 50 percent of the vote."

Utah Republican Party Chairman James Evans said he thinks Trump's margin will grow between now and Election Day.

"Fifteen points is still too close," Evans said. "You're starting to see this now, more and more people are starting to publicly support Trump. The last couple of weeks have been pretty good for him and you're going to see a greater spread there."

Trump is indeed unpopular in the state, with 61 percent of Utah voters having an unfavorable impression of the GOP nominee. But even with those dismal marks, he continues to be considerably more popular than Clinton, who is viewed negatively by 72 percent of those surveyed.

Even President Barack Obama, who lost Utah by more than 40 points in 2012, fares 10 points better than Clinton in a hypothetical head-to-head with Trump.

"There are states that are an easier lift than winning Utah where we've got to invest resources, and we will," Sullivan said. "But we can make the case to people here that you may not agree with Hillary Clinton on every issue under the sun, but she's a person who can work with people from all different perspectives to improve the lives of families and that Donald Trump is fundamentally unfit and unqualified to be president of the United States and everyone should be doing their part to make sure that he's not."

Evans said Democrats are trying hard to create an anti-Trump narrative, but "Just because they keep saying that, doesn't mean it's true."

He also scoffed at the notion that Clinton is able to work across the aisle.

"Who can work with Hillary when you can't believe anything she says?" Evans said.

Forty-eight percent said that Trump could not be trusted to control the U.S. arsenal of nuclear weapons.

Fifty-six percent of Mormons dislike Trump, but an overwhelming 84 percent have an unfavorable opinion of Clinton. Just 12 percent of Mormons would vote for Clinton, tying her with Johnson and putting her behind McMullin at 13 percent and Trump at 44 percent.

The polling firm said that, were it not for Mormons in the state, Utah would be among the most Democratic states in the country, because Clinton leads Trump by 16 points among non-Mormons, 46 percent to 30 percent.

Nearly two-thirds — 65 percent —¬†of Utahns believe Trump should release his tax returns, which he has refused to do, thus far.

Meanwhile, 65 percent of Trump supporters say that if he loses the election, it will be because it was "rigged" in favor of Clinton.

Though he trails significantly, McMullin's campaign has high hopes.

"It is humbling to have the support of thousands of Utahns who are attracted to a positive candidate and optimistic about our country," said Joel Searby, McMullin's chief strategist. "We have much work ahead and intend to win in November."

Outside of the presidential election, other statewide Republican candidates in Utah would all win easily if the election were held today.

Gov. Gary Herbert leads Democrat Mike Weinholtz by a margin of 57 percent to 21 percent, with a similar 57 percent of Utahns approving of the job Herbert is doing as governor. Sixty-nine percent of those surveyed had no opinion of Weinholtz.

Just 42 percent of Utahns approve of the job U.S. Sen. Mike Lee is doing, but he holds a 30-point lead over first-time candidate Misty Snow, 51 percent to 21 percent. In a hypothetical head to head with former Rep. Jim Matheson, Lee would beat the congressman-turned-lobbyist, 44 percent to 37 percent.

Public Policy Polling surveyed 1,018 likely voters — 80 percent of them via landline phone calls — from Aug. 19-21. The margin of error is plus or minus 3.1 percentage points.

Twitter: @RobertGehrke