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Washington • Less than a week after announcing his bid for a Senate leadership post, Utah's Mike Lee reversed course, leaving incumbent Sen. John Barrasso as the only candidate for the chairmanship of the Republican conference's policy committee.

"In the interest of party unity, Senator Lee is ending his campaign for Republican Policy Committee Chair at this time," Lee spokesman Conn Carroll said Tuesday.

Lee had believed that Barrasso, a Wyoming Republican, was term-limited from serving as the policy chair, the fourth-highest position in Senate leadership, and Lee declared his bid for what he thought would be an open seat.

But Senate Majority Leader Mitch McConnell said Barrasso started serving mid-term in 2012 and could therefore serve another two-year stint. Sen. Orrin Hatch, Lee's Utah colleague, had already said he would back Barrasso before Lee entered the race and stuck by his commitment.

In a letter to colleagues on Sunday, Lee reportedly withdrew his name from consideration for the spot, which had set up a battle between the tea-party darling and the established Senate leaders. Lee's office refused to release the letter.

FreedomWorks, an umbrella group for the tea party movement, said it was disappointed to see Lee pull back his bid but that at least he's put down his marker to take on the role in the future.

"I guarantee you, the next time there is a fight like this, [Lee will] be the first person reporters call up and say are you going to run again," said Adam Brandon, chief executive officer of the group.

Brandon said in an interview that Senate strategists should have realized that the reason there's such an antagonistic relationship between elected officials and the base is because leaders don't want to bring in voices like Lee. That won't last forever, he said.

"I know that in the future, Mike Lee is going to be that policy leader in the Senate," Brandon said. "When this election is over, he is going to be one of the emerging voices standing for the entire Republican Party."

Also Tuesday, the GOP conference met for its weekly lunch and backed McConnell's decision that leaders can serve three, two-year terms but that does not count partial terms.

"The conference decided to keep its current precedents regarding term limits for leadership offices," McConnell said after. "No changes were made."

The Senate GOP leadership team is made up of McConnell of Kentucky, Majority Whip John Cornyn of Texas, Conference Chairman John Thune of South Dakota, Vice Chairman Roy Blunt of Missouri and Barrasso.

Hatch, the longest-serving Republican senator, is the Senate president pro tempore, technically the highest ranking official in the Senate next to the vice president but the role does not set the agenda for the majority.