There might be no Congressional candidates in the country with a more vested interest in Mitt Romney being the GOP presidential nominee than Republicans running for Utah’s new 4th district, where Democratic Rep. Jim Matheson is seeking a seventh term.

Republican candidates, elected officials and consultants in the state believe Romney can improve turnout among Republican and independent voters for what’s expected to be among the most competitive races in the country.

“People in Utah are so tied to Romney, they’re so grateful for what he did in saving the Olympics,” Republican consultant Brian Chapman said. “If Romney is the nominee, you will have a massive turnout of Republicans in Utah that overwhelm any Democrat.”

GOP state Rep. Stephen Sandstrom said the 4th is undoubtedly “the hardest district for a Republican to win,” but he’s confident he can unseat Matheson. “I think this is going to be a Republican year, not just across the nation, but specifically in the state of Utah,” he said. “And with Mitt at the top of ticket, it will be an even more Republican year in Utah.”

None of the four districts drawn by the GOP-controlled Legislature were advantageous for a Democrat, but the Salt Lake County-based 4th gives Matheson his best shot at returning to Congress for a seventh term. It leans Republican — Sen. John McCain (R-Ariz.) would have won 56 percent there in 2008 — and includes only about a quarter of Matheson’s current district. But Democrats remain confident, thanks to his moderate voting record and history of winning in tough districts.

“These are really independent voters, and Jim Matheson is really independent,” state Democratic Party Chairman Jim Dabakis said. “It’s a match made in heaven.”

In an interview, Matheson said living outside the district and being forced to campaign for a significant portion of voters he doesn’t currently represent will not be prohibitive to winning. He won’t be forced to totally introduce himself to a new population thanks in part to the state’s sole media market and the fact that 85 percent of the district is in Salt Lake County, where he lives.

“The issues I talk about and the approach I take to the job really don’t change based on the particular boundaries of this district,” Matheson said. “I think people in this district are quite familiar with me.”

Matheson was one of 12 Democrats in 2010 to win districts carried two years earlier by McCain in the presidential contest. After watching several of his Blue Dog Coalition colleagues in GOP-leaning districts defeated in the last election, Matheson said he’s not taking anything for granted.

Although the 4th provides him the “best opportunity” to continue serving in Congress, he said, “I’ve got to work real hard to win this district.”

There are at least three legitimate GOP contenders. Saratoga Springs Mayor Mia Love last week became the latest to formally enter the race, joining Sandstrom and state Rep. Carl Wimmer.

They’re all competing in the April 21 state party convention, where the top two vote-getters among the district’s delegates advance to a June primary unless one candidate receives 60 percent of the vote. The process begins March 15, when delegates are elected at 1,850 local caucuses statewide.

Wimmer already has the backing of Sen. Mike Lee (R-Utah) and conservative groups including the Club for Growth, Citizens United and the Family Research Council, leading some insiders to believe he’s the early frontrunner. Lee is hosting a fundraiser for Wimmer on Jan. 17 in Utah.

“The bottom line is I have the message and campaign structure and the ability to defeat Jim Matheson,” Wimmer said. “The delegates understand that to defeat Jim Matheson, it’s going to require a complete campaign structure, and part of that is fundraising.”

Wimmer said he raised more than $200,000 through the end of 2011, and he resigned his state House seat last week because of rules prohibiting state legislators from fundraising while the Legislature is in session.

Sandstrom, who will not resign his seat, is well-known for the illegal-immigration enforcement bill he sponsored that was signed into law last year. Sandstrom had loaned his campaign $62,000 through September and said the fundraising prohibition will not hurt him in the race.

Wimmer and Sandstrom said they are focusing their message on defeating Matheson but that they’re also looking to build a coalition for the convention.

“Right now we’re having events and things like that, but we’re targeting people that we want to be delegates,” Sandstrom said. “So, certainly, you try to get your supporters to become delegates. And you have to have a ground game for that.”

If elected, Love would be Utah’s first African-American Member of Congress and the first African-American Republican woman in Congress. Love has the backing of Rep. Allen West (R-Fla.), the only Republican member of the Congressional Black Caucus.

“My job is to just get to the delegates and speak to the delegates, and we’re doing that,” Love said. “That’s the game, that’s the plan. Get to as many delegates as possible and let them know who I am.”