President Donald Trump is downplaying his frustrations with a key Republican senator, according to a recent report.Despite a recent public spat, Trump has privately said that Senate Majority Leader John Thune is giving him more trouble than he's let on, wrote Jonathan Lemire in a Tuesday piece for The Atlantic.A senior adviser told Lemire that Trump considers Thune "one of my biggest headaches." The frustration with Thune spilled into public view last week, when White House press secretary Karoline Leavitt said that the president's "patience is running out" with Thune. During an event in Georgia that week, Trump also called Thune out as he told attendees to call Thune and demand he pass the SAVE America Act, a stalled voting bill.Lemire noted that Trump told reporters aboard Air Force One on Monday that his relationship with Thune was "fine," however. Axios also reported on Tuesday that Thune plans to attend Trump's midterm GOP convention in Dallas.Trump's problems with Thune stem from White House pressure on Republicans to gut the filibuster and push through the SAVE America Act, per Lemire. Trump has demanded that the Senate eliminate the 60-vote threshold to pass the SAVE Act, which would require voters to provide proof of citizenship and, critics warn, make casting a ballot harder. Thune has refused to blow up the filibuster to do it.Lemire pointed out that Thune's resistance contrasts with how "the GOP marched in lockstep to pass the One Big Beautiful Bill Act tax legislation" last year.White House spokesperson Abigail Jackson reiterated to Lemire that the SAVE Act "has always been a top priority for President Trump and it remains one." She added that Trump "will not stop fighting until it is passed."