Sen. Mike Enzi (R-Wyo.) has a significant lead over primary challenger Liz Cheney, according to the first polling released on the 2014 U.S. Senate race in Wyoming.

Enzi is ahead of Cheney by 55 percent to 21 percent among GOP primary voters, according to the Republican firm Harper Polling, which conducted the survey for the Conservative Intelligence Briefing blog. His favorable rating is 76 percent among Wyoming Republicans, with just 6 percent viewing him unfavorably.

Forty-eight percent say Enzi has done enough to deserve a fourth term, while just 28 percent think someone else should have a chance.

Enzi won more than 75 percent of the vote in his 2008 reelection, but raised a relatively low $1.6 million. He told CNN Wednesday that he puts little stock in polls, but expects his constituents to give him another term.

"I don't have to do a poll. I've never done a poll. I can tell from the conversations I've had," he said.

Cheney, who declared her candidacy Tuesday, told the Associated Press that it was time for "a new generation to come to the fore."

"I don't see seniority as a plus, frankly," she said.

While Cheney is generally well-liked in Wyoming, many of the state's Republicans have yet to make up their minds about her: 45 percent view her favorably, 15 percent unfavorably, and 40 percent say they haven't heard of her or don't have an opinion.

Her father, former Vice President Dick Cheney, has a reputation to rival Enzi's, with 74 percent of Wyoming Republicans giving him a favorable rating. The elder Cheney represented the state in the U.S. House of Representatives for a decade.

Wyoming's voters tend to give their leaders high marks.

"There’s no state in the country that loves its politicians like Wyoming," Dean Debnam, president of the Democratic firm Public Policy Polling, said in 2011, one of the last times the GOP-dominated state was polled. "It has the most popular governor and [two] most popular senators we've ever polled on anywhere."

The Harper poll used automated phone calls to survey 422 likely Wyoming Republican voters on July 17 and 18.

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