Senate Majority Leader John Thune is pulling off something today's Republicans rarely attempt: telling President Trump "no."Why it matters: Pressure from Trump and the MAGA base is piling up on Thune (R-S.D.), especially over a voter ID bill, but he has an important insurance policy: GOP senators have his back."I think he's got strong support. I read all the stories, but I think mostly that's made up by reporters," Sen. Mike Crapo (R-Idaho) told Axios. "Leaders absorb some of the punishment, but I think he's doing great. No one could do a better job than he is right now," Sen. Roger Marshall (R-Kan.) told Axios."His cred in the conference has never been stronger," Sen. Kevin Cramer (R-N.D.) told Axios.Catch up quick: Trump's frustration with Thune over the inability to pass the SAVE America Act or nuke the filibuster is, again, bubbling over."Thune should not allow the United States Senate to 'leave town' until it passes The Save America Act or, far better still, TERMINATES THE FILIBUSTER," Trump demanded on Truth Social on Monday morning.Thune has snapped back, reiterating that it is a matter of math. There are not enough votes to pass SAVE, end the filibuster or justify canceling the August recess."Give me a rationale or a path to getting success, staying here through the month of August," Thune told reporters Monday about the calls from Trump and a few GOP senators to cancel recess to pass SAVE. "You could stay here til Christmas."What to watch: Trump has not called for Thune's ouster. He even told reporters Monday that their relationship is "fine." But the building anger has fueled widespread speculation in D.C. that the president could eventually go there.Even if he does, it would not carry the same weight as a threat to Speaker Mike Johnson's leadership in the House.For one, Senate leadership elections are conducted by private ballot, giving more cover to senators who may not want to publicly cross Trump.What we're hearing: Many Republican senators are quick to share their support for Thune behind closed doors, even if not all are willing to publicly do so right now.Thune "is not in jeopardy," a GOP senator told Axios, requesting anonymity to speak candidly. "He is not the problem.""We have a bunch of people across Capitol Hill that are obsessed with social media fame," another senator told Axios, referring to those questioning Thune's leadership.Senior GOP aides for other senators also tell Axios the problem is really "squeaky wheels" getting more attention and that the situation could ultimately benefit Thune within the conference.The other side: A conservative corner of the conference is certainly growing frustrated with Thune. Seven senators are now calling to delay the August recess until SAVE is passed: Mike Lee (R-Utah), Rick Scott (R-Fla.), Ashley Moody (R-Fla), Jim Banks (R-Ind.), Tommy Tuberville (R-Ala.), Bill Hagerty (R-Tenn.) and Darline Graham (R-S.C.)But even some of them admit Thune's leadership is not at stake."I wouldn't say that, because his job lies with us," Tuberville said when asked about any risk to Thune's position as leader. "But a lot of people are getting a little bit frustrated." The bottom line: "I've been somewhat disappointed more Republican senators haven't been bold enough to speak out," Cramer said.— Axios' Kate Santaliz contributed to this story.