Senate Republicans piled on conservative Sen. Mike Lee Michael (Mike) Shumway LeeMcConnell shores up GOP support for coronavirus package McConnell tries to unify GOP Davis: The Hall of Shame for GOP senators who remain silent on Donald Trump MORE (R-Utah) during a private meeting Thursday, rebuking him after he pressed several GOP leaders earlier in the week to step down from leadership roles because of term limits.

Colleagues scolded Lee for lacking collegiality by trying to enforce a GOP conference rule that allows lawmakers to serve only three terms in the elected leadership, according to lawmakers who attended the heated discussion.

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Lee has argued their time is up, while Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellObama calls on Senate not to fill Ginsburg's vacancy until after election Planned Parenthood: 'The fate of our rights' depends on Ginsburg replacement Progressive group to spend M in ad campaign on Supreme Court vacancy MORE (R-Ky.) says they should be allowed to stay in leadership through the end of 2018.

The leaders affected are Senate GOP Conference Chairman John Thune John Randolph ThuneWhat Senate Republicans have said about election-year Supreme Court vacancies The Hill's 12:30 Report - Presented by Facebook - Don't expect a government check anytime soon The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Trump contradicts CDC director on vaccine, masks MORE (S.D.), Republican Policy Committee Chairman John Barrasso John Anthony BarrassoOVERNIGHT ENERGY: Democrats push resolution to battle climate change, sluggish economy and racial injustice | Senators reach compromise on greenhouse gas amendment stalling energy bill | Trump courts Florida voters with offshore drilling moratorium Senators reach compromise on greenhouse gas amendment stalling bipartisan energy bill The Hill's Morning Report - Sponsored by National Industries for the Blind - Trump, Biden battle over vaccine, economy; Congress returns MORE (Wyo.) and conference vice chairman Roy Blunt Roy Dean BluntCDC tells Congress it urgently needs billion for vaccine distribution On The Money: Trump undercuts GOP, calls for bigger COVID-19 relief package | Communities of color hit hardest financially by COVID-19 | Businesses, states pass on Trump payroll tax deferral Trump undercuts GOP, calls for bigger COVID-19 relief package MORE (Mo.).

Lee has told colleagues that he is running for Barrasso’s job on the assumption he will have to vacate it at year’s end. He says he will not challenge Barrasso directly, but he’s not giving up on his effort to persuade GOP colleagues to apply a term limit to end his tenure in 2016.

Some GOP senators accused Lee, a favorite of Tea Party groups and conservative activists, of fomenting internal frictions at a time when they should be unified and focused on the challenge of keeping their majority.

Senators also criticized Lee’s leadership of the Senate Republican Steering Committee, which hosts a weekly lunch and promotes conservative policies.

One lawmaker said it became clear in the meeting that Lee would lose by a big margin if he squared off against Barrasso, noting the Wyoming senator is very popular with colleagues.

Walking out of the lunch, Sen. Johnny Isakson Johnny IsaksonLoeffler: Trump 'has every right' to fill Ginsburg vacancy before election Bottom line New poll shows tight presidential race in Georgia MORE (R-Ga.) patted Barrasso on the shoulder and assured him, “You’re in good shape.”

But if Lee can steer the discussion to the question of applying term limits evenly across the leadership, then he might be able to win Barrasso’s job while avoiding a popularity contest.

Behind closed doors, McConnell reminded Lee that he and his close friend, Sen. Ted Cruz Rafael (Ted) Edward CruzSenate Republicans face tough decision on replacing Ginsburg Cruz: Trump should nominate a Supreme Court justice next week Renewed focus on Trump's Supreme Court list after Ginsburg's death MORE (R-Texas), who is running for president, received waivers a few years ago to serve on the Judiciary Committee and should now show some collegiality to their colleagues in leadership.

Senate Republican rules do not allow two members from the same state to serve on a committee, and fellow Utahan Orrin Hatch Orrin Grant HatchBottom line Bottom line Senate GOP divided over whether they'd fill Supreme Court vacancy MORE (R) has long served on the Judiciary panel. The conference voted to waive the rule for Lee.

Lee was granted a waiver to serve on Judiciary at the beginning of 2011, but did not receive waivers at the start of the 113th Congress in 2013 or the 114th in 2015. Cruz received his waiver at the start of 2013 but not at the beginning of this Congress.

Therefore, in McConnell’s view, they both continue to serve on the panel by the grace of their colleagues’ good will.

One GOP aide, however, emphasized the fact that Lee needed a waiver in the first place to serve, in spite of the rules, and argued the same should apply to Barrasso and other leaders.

“The thing I heard from lunch today was that McConnell surprisingly agreed that a waiver was needed for Barrasso, Blunt and Thune to run for another term. He apparently compared it to the waivers the conference sometimes votes to make certain committee assignments,” said a Republican aide familiar with the lunch.

Sen. Bob Corker Robert (Bob) Phillips CorkerHas Congress captured Russia policy? Tennessee primary battle turns nasty for Republicans Cheney clashes with Trump MORE (R-Tenn.) accused Lee’s staff on the Republican Steering Committee of coordinating with outside groups to oppose compromise bills put together by Republican senators, according to sources who attended Thursday’s meeting.

Republican senators say the Steering Committee, which Lee has chaired since the beginning of January, does not represent the entire conference, as some believe it should.

Corker argued that it’s counterproductive for an internal Senate policy group funded with dues from GOP senators to stake out positions against bills championed by those member senators.

Conservatives recently criticized Corker’s new bill to combat human trafficking, the End Modern Slavery Initiative Act, as something that would create a redundant government program and possibly facilitate funding for abortions.

An anonymous senior Republican aide told The Daily Signal this month: “There are real concerns that the bill lacks sufficient pro-life statutory protections and would create a foundation that could use non-federal donations to fund groups that provide abortions.”

The Heritage Foundation, a conservative think tank, recently published a policy brief warning that Corker’s bill lacked sufficient safeguards to prevent money raised by private organizations to fight trafficking from being used to promote abortion.

“The United States cannot stand up to a global human trafficking industry that violates the basic human rights of millions around the world unless it recognizes the worth and dignity of all victims of human slavery, including unborn children, and defends their basic right to life,” the brief stated.

Corker’s concerns are shared by other senators.

“Generally speaking, any effort that would encourage outside groups to weigh in on internal discussions is not healthy,” said Sen. Lisa Murkowski Lisa Ann MurkowskiSenate Republicans face tough decision on replacing Ginsburg What Senate Republicans have said about election-year Supreme Court vacancies McConnell says Trump nominee to replace Ginsburg will get Senate vote MORE (R-Alaska), when asked about coordination between Senate staff and outside groups. She declined to talk about Thursday’s meeting.

As the discussion heated up, Lee’s colleagues seized the opportunity to also sound off against the Senate Conservatives Fund, the right-leaning political action committee that has targeted Senate Republican incumbents in the past.

They made it clear that they associate Lee’s efforts to promote conservative policies with the political attacks waged by outside groups.

The Senate Conservatives Fund praised Lee at the beginning of the election cycle as “exceptional” and solicited contributions for his reelection campaign.

Sen. Thom Tillis (R-N.C.) questioned the timing of Lee’s leadership bid and why it became immediately reported on in the press, according to sources in the room.

Tillis argued that it has become a needless distraction at a time when senators need to concentrate on the upcoming election, when their majority will be at stake. He believes Lee’s conversation with colleagues about his leadership ambitions should have remained private.

Tillis, who served as speaker of the North Carolina House of Representatives from 2011 to 2015, said leaders in legislative bodies must know how to foster unity if they are to be effective.

This post was updated at 6:46 p.m.