"What he said about John, I think, was offensive. He's becoming a jackass at a time when we need to have a serious debate about the future of the party and the country," Graham told CNN's Kate Bolduan. "This is a line he's crossed, and this is the beginning of the end of Donald Trump ... I am really pissed."
On Saturday, Trump -- at a GOP political event in Iowa -- said McCain was "not a war hero."
"He is a war hero because he was captured," Trump added. "I like people that weren't captured, OK? I hate to tell you. He is a war hero because he was captured. OK, you can have -- I believe perhaps he is a war hero."
Bipartisan elected officials from the White House all the way to the wide open Republican primary field are using incendiary comments from Trump to praise former prisoner-of-war McCain.
Former Florida Gov. Jeb Bush broke from his prepared remarks of a policy speech Monday to declare that McCain is a "real hero," as Donald Trump insists that he owes no apology to McCain for questioning the Arizona senator's military heroism.
Trump, who's experienced a bump in the polls since announcing his presidential bid last month, is known for his unfiltered rhetoric, but the comments made at an Iowa voter forum from over the weekend drew immediate and near universal rebuke from other elected officials and candidates.
Making his pitch for reforming Washington, Bush said Monday in Tallahassee that he supports a proposal by McCain, who chairs the Senate Armed Services Committee, to change the defense procurement process.
When Bush mentioned McCain's name, he interjected to describe the former GOP presidential nominee as "a real hero, by the way." The audience, largely comprised of his former associates from his days as governor, broke out into huge applause.
Shortly after Bush's comments, White House Press Secretary Josh Earnest said that despite the difference between President Barack Obama and his former campaign rival McCain, "have not reduced (Obama's) appreciation for Sen. McCain's remarkable service to the country," adding Obama had "deep respect for Sen. McCain's heroism."
Responding for the first time himself, McCain said Monday morning that he didn't feel Trump owed him an apology, suggesting instead the billionaire real estate developer apologize to American veterans.
"... I think he may owe an apology to the families of those who have sacrificed in conflict and those who have undergone the prison experience in serving our country," McCain told MSNBC's "Morning Joe".
Bush was quick to defend McCain on Twitter on Saturday, when Trump stirred controversy by saying McCain wasn't a war hero because he was captured.
"Enough with the slanderous attacks. @SenJohnMcCain and all our veterans - particularly POWs have earned our respect and admiration," he tweeted.
And Bush was by no means the only 2016 candidate condemning Trump's comments. Democratic front-runner Hillary Clinton, as well as Republican Sens. Marco Rubio and Lindsey Graham condemned the remarks.
"It's not just absurd, it's offensive" Rubio said in an interview Sunday with CNN's Jake Tapper on "State of the Union." "It's ridiculous. And I do think it's a disqualifier as commander-in-chief."