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Washington • Sen. Mike Lee is making a bid for Senate leadership, seeking the job as chairman of the Senate Republican Policy Committee, the fourth highest spot in the GOP caucus.

But the Utah Republican faces competition from incumbent chairman, Sen. John Barrasso of Wyoming, who has the backing of Majority Leader Mitch McConnell, R-Ky., and Sen. Orrin Hatch, R-Utah. Lee announced his intentions this week, earning the support of at least one conservative group but raising concerns from others as to why he would challenge Barrasso.

"I was quite surprised, because I've committed to John Barrasso," Hatch told Politico on Tuesday. "I don't want you to report it as I'm taking on Lee. I didn't know he was going to run. I'm already committed to John Barrasso so I'm going to live up to the commitment."

The policy committee chairman, who leads what is essentially the in-house think tank for GOP senators, is limited to three, two-year terms, and Barrasso began serving in 2012, midterm, leaving him open for another two-year tenure, according to Senate leadership aides.

Lee's office says that it believed the seat would be open because Barrasso would have served three times, and that Lee wouldn't be trying to take on the incumbent. Lee has now called 30 members, his office says, and only one senator has offered negative feedback.

Barrasso's office didn't address Lee's bid for the leadership spot but noted the Wyoming senator wants to keep his gig.

"It seems too early to be talking about leadership elections when so much remains to be done," said Barrasso spokesman Bronwyn Lance Chester. "Senator Barrasso is focused right now on keeping the Senate majority this fall. However, at the right time, later in the year, he will talk to his colleagues about the future. Senator Barrasso continues to want to serve the Republican conference, and there will be plenty of time to discuss that."

Lee says he's positioned well for being a Senate leader — he currently serves as a counselor to McConnell as chairman of the Senate Steering Committee — and the move would help Utah.

"Utah is truly a pioneer in public policy innovation," Lee said in a statement. "As policy committee chair, I can both elevate Utah nationally and help the country by highlighting all the great things being done in our home state."

Asked about Lee's bid, McConnell spokesman Don Stewart said that Barrasso, as well as Senate Conference Chairman John Thune of South Dakota and Vice Chairman Roy Blunt of Missouri, are eligible to run again.

"The [majority] leader believes they've all done a great job," Stewart said, "and he hopes that they do all run again."

Lee's plans are already earning praise among some conservative compatriots.

"Republicans must be mindful that we need to advance sound policies grounded in constitutional and limited-government principles," said FreedomWorks CEO Adam Brandon. "Senator Lee has pursued a conservative reform agenda that appeals to Americans from all walks of life. His agenda promotes pro-growth policies, upward mobility, ends crony capitalism, reforms the justice system, and protects our precious freedoms."

FreedomWorks is a tea-party group that has supported Lee for years.

Lee has attempted to remake himself into the Senate's idea man — pushing bipartisan issues such as criminal-justice reform — after he earned a rebuke from fellow senators in 2013 by orchestrating a vote to cut funding for the Affordable Care Act tied to the federal budget. The result was a 16-day government shutdown. The other architect of that controversial strategy was Sen. Ted Cruz, the Texan now seen by many Republicans as the best hope of stopping Donald Trump in the GOP presidential chase.