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DENVER — On Tuesday, when Congressman Cory Gardner announced he would not be running against Democratic U.S. Sen. Mark Udall, he was actually just the latest top-tier Republican to opt against a run next year.

“I’ve got more work to do for the people of the 4th Congressional District,” Gardner, R-Yuma, told FOX31 Denver Tuesday afternoon. “And I needed to make a decision. People are making their decisions and the field needed to know.”

The Republican field, at the moment, is nonexistent.

And FOX31 Denver has learned that other would-be candidates who Republicans in Washington are trying to recruit are also saying no.

“They’re thinking outside the box, but they’re striking out in trying to find a Major League candidate to run against Udall,” one Washington operative told FOX31 Denver.

Republicans have reportedly approached retired four-star Gen. Gene Renuart, who last served as commander of U.S. Northern Command and NORAD in Colorado Springs before retiring in 2010.

“A four-star general certainly would inspire a lot of confidence,” Colorado GOP Chairman Ryan Call told FOX31.

But Renuart has apparently indicated that he isn’t interested in challenging Udall, who serves on the Senate Armed Services Committee.

The National Republican Senatorial Committee tells FOX31 Denver that it hasn’t contacted Renuart.

The NRSC does acknowledge approaching Colorado Solicitor General Dan Domenico, who has served in the role since 2006 and argued a case before the U.S. Supreme Court in 2012, about taking on Udall.

“He’s very impressive,” Call said. “And his wife has been a prolific fundraiser for us.”

But Domenico isn’t interested either.

Colorado Treasurer Walker Stapleton was also approached about the U.S Senate race, but he’s more interested in state-level office than a move to Washington, sources say.

Attorney General John Suthers, who is term-limited next year and has ruled out a run for governor, may still be a possibility.

If Republicans cannot recruit a candidate, they’ll likely leave the field to former Congressman Bob Beauprez, who lost badly in his 2006 gubernatorial bid but was a fixture on the campaign trail last year stumping almost daily across Colorado on behalf of presidential hopeful Mitt Romney.

“He would be a very credible candidate,” Call told FOX31 Denver earlier this month.

“He’s smart, he’s got money, he’s a hard worker,” said Michael Sozan, who’s serving as Udall’s unofficial campaign manager. “He’s someone Mark would take very seriously.”

Another possibility could be state Sen. Randy Baumgardner, R-Hot Sulphur Springs, who has been expressing some interest in taking on Udall.

“I’m exploring my options,” Baumgardner told FOX31 Denver on Wednesday. “I’m not really prepared to say more than that, but I am looking at it.”

Udall, meanwhile, keeps chugging along.

The first-term senator has $2.5 million cash on hand after a strong first quarter of fundraising and he is the only swing state Democratic senator facing reelection in 2014 without any declared opponent.

But Gardner offered an idea of how a Republican challenger, whenever one materializes, may go after Udall.

“He cast the deciding vote for Obamacare,” Gardner said. “He’s going to have to explain that vote just as we’re going through implementation.”