Utah Democrats made a gamble, betting that a conservative independent would have a better chance of winning the Utah Senate race than a Democrat. Now, they are seeing glimmers of hope for their Hail Mary.

A former CIA agent and congressman, Evan McMullin, is running to unseat Senator Lee, pitching himself as a moderate conservative and arguing that Mr. Lee, a conservative Republican, is too extreme.

The Utah Democratic Party declined to nominate its own candidate, instead throwing in with Mr. McMullin, whom they are backing in no small part because of his criticism of President Trump.

Before the primary, Congressman Ben McAdams, a Democrat, explained the thinking to UTPOL Underground, saying, “There’s too much at stake in this election for us not to try something new.”

“The path to pushing back on this far-right surge that we’re seeing in Utah is for independents, Democrats, and moderate Republicans to join together to say, ‘That’s not who we are and that’s not what Utah is’,” he said.

Mr. McMullin made a name for himself as an anti-Trump conservative in the 2016 election, when he ran for president with the stated goal of winning his home state and taking electors away from Mr. Trump.

He ended up winning only 22 percent of the state’s vote, while Hillary Clinton won 27 percent and Mr. Trump carried 46 percent. This year, however, there are signs that his campaign may perform better.

A new poll from Hiss Research Consultants is showing Mr. McMullin ahead of Mr. Lee by a margin of 49 percent to 43 percent. The Libertarian Party candidate, James Hansen, is polling at 4 percent.

Hiss’s finding is an outlier. Most polls are showing Mr. McMullin behind Mr. Lee. FiveThirtyEight’s average of polling shows Mr. Lee 4.5 points ahead. Mr. Lee’s campaign, however, is showing some signs that it is worried.

Tuesday night, Mr. Lee went on “Tucker Carlson Tonight” to criticize Mr. McMullin. He called on Senator Romney to support his campaign.

“Mitt, if you’d like to protect the Republican majority — give us any chance of seizing the Republican majority once again — getting it away from the Democrats,” he said. “Please get on board. Help me win re-election.”

Mr. Romney, who has recently supported bills that Mr. Lee opposed concerning gun control, semiconductor manufacturing, and infrastructure, declined to endorse either candidate, saying “both are good friends.”

Mr. Trump has come to Mr. Lee’s defense in a statement issued Wednesday, saying that Mr. Romney has “abused” Mr. Lee.

“Mike Lee is an outstanding senator who has been abused, in an unprecedented way, by a fellow Republican senator from his own state, something which rarely has happened in political history,” Mr. Trump said.

The Club for Growth, a conservative political action committee, also appears to be concerned about Mr. Lee’s odds, having dropped $2.2 million into a relatively underfunded race.

“We think it’s critical Mike Lee win this race and win it handily,” the  Club for Growth president, David McIntosh, said. “We will continue to spend to bring Utah voters the truth about Mike Lee and Evan McMullin.”

While some signs are pointing toward a more competitive race, many who watch closely remain skeptical of Mr. McMullin’s chances. Among them is a political scientist at the University of Utah, James Curry.

“I wouldn’t read much into two polls showing McMullin has a narrow lead when the preponderance of polls still show Lee with a comfortable lead,” he tells the Sun. “I don’t really see much change from summer.”

Mr. Curry also identifies another issue: Should Mr. McMullin win in Utah, he is probably not a reliable vote for Democrats. Citing the fact that Mr. McMullin was once a Republican, he asks, “What exactly do they stand to gain?”

“Even if McMullin does win, I think it’s still not a savvy move for Democrats,” he tells the Sun. “They’d be trading in Lee for another Republican, who is on some issues even more conservative.”

Although Mr. McMullin has repeatedly said he wouldn’t caucus with either Democrats or Republicans, Mr. Lee and his campaign has tried to capitalize on the issue, painting him as “a Democrat running in disguise.”

For Utah voters, electing Mr. McMullin could limit their influence on policies, and a refusal to caucus with either Democrats or Republicans could sideline Mr. McMullin in policy discussions.