The White House’s growing frustration with Senate Majority Leader John Thune seeped into public again on Thursday, the second consecutive day team Trump has vented at the chamber’s Republican leader. “His patience is running out,” White House press secretary Karoline Leavitt said, referring to President Donald Trump's feelings about Thune. “He wants to see as much of the SAVE America [Act] passed as possible by the August recess.” The White House press secretary’s rare criticism of a majority leader from the same party as a sitting president came one day after Trump complained about Thune’s job performance near the end of an event in Marietta, Ga. During that event, Trump groaned to a friendly audience about the Senate being unable to clear a 60-vote threshold on the SAVE America bill, a package of GOP-crafted elections changes that critics say would represent an unprecedented level of federal involvement in election administration. “Everybody call John Thune at the Senate. He’s the leader of the Republican Party. And tell them to get this stuff approved,” he told the crowd. “So we're fighting so that all voters must show voter ID. We're fighting so that all voters must provide proof of citizenship, OK? And also the no mail-in ballots, very important.” In the lead-up to his call for a Thune phone blitz, Trump grew agitated when talking about the Senate’s 60-vote threshold. “They got to really terminate the filibuster, get everything approved right away, because you're going to have a stoppage. You're going to have a stoppage in September,” he said, warning of a government shutdown when funding potentially lapses on Sept. 30. “The Democrats won't approve [any]thing. They’ve become deranged. … They should terminate the filibuster.” Thune on Thursday pushed back on the press secretary’s comments, saying Leavitt or “somebody else” should “get on the phone and get the votes.” “Instead of, you know, pointing the finger at Republicans, they might think about going after the people who are stopping it on the floor, which is the Democrats,” he said. “And if there are Republicans that they think are gettable, get on the phone. Let's get them to ‘yes.’” At least two GOP senators took umbrage with Leavitt’s statement. “I have 1,000 percent confidence in Thune, and anybody in the White House who thinks he's not a good leader isn't qualified for their job,” retiring North Carolina Sen. Thom Tillis told reporters. “We just don’t have the votes,” said Sen. John Cornyn, a Texas Republican who lost to a Trump-backed opponent in the primary, referring to the election bill. “There’s nothing that Senator Thune can do to change that. This idea that [Trump] can just command members of the Republican Conference to get in line is just a fantasy.” Earlier that day, in the White House briefing room, Leavitt said that Trump “knows that's what the American people want to see passed,” adding: “They want proof of citizenship in our elections, and the President feels very strongly about that.” “The American people … elected, overwhelmingly, Republicans to lead — not just this White House, but also the House and the Senate. The House did its job,” she added, referring to that chamber passing the SAVE bill. “The Senate needs to do its job, too.” But Thune Thursday reiterated the difficulties of passing SAVE in the Senate, including using the budget reconciliation process. The House adopted a GOP-backed budget resolution along party lines Wednesday with funding to incentivize states to adopt portions of the legislation. “If there's an opportunity to deal with a budget resolution, the SAVE Act to get through a Byrd bath would have to be very carefully structured based upon incentive, mostly grant money,” Thune said. “Depending on that structure, whether or not we can get much of it included in a budget resolution, is still an open question.” “We're going to do everything we can to move that forward,” he continued. “But as I’ve told you before, the math on that hasn't changed, and it's still likely to be a 60-vote exercise…I can't count 50 right now on a budget resolution.” During his exchange with reporters at the Capitol, Tillis was more blunt, telling reporters “we're wasting our time and we're being dishonest to the American people to say that we need SAVE Act passed because there's no way on God's green earth it can be implemented by this election.” Cornyn, meanwhile, argued the debate has further damaged Republicans’ chances of retaining a congressional majority after November. “I don't know who it was that sold the president on this idea that this was attainable, but it's creating a circular firing squad for Republicans,” he said. “And here we are, what? One-hundred and three days before the midterm elections? “And this is not a great place for us.”