But Trump simply may not care; indeed he seemed to bask in his McCain takedown.
After dismissing McCain's reputation as a war hero because he was captured in Vietnam and "I like people who weren't captured," Trump declared "I will say what I want to say." He insisted he would stay in the GOP primary field, despite rivals who say he's now shown he doesn't merit the presidency.
"It's not just absurd," Florida Sen. Marco Rubio. "It's offensive. It's ridiculous. And I do think it is a disqualifier as commander in chief."
Numerous other GOP candidates, including Jeb Bush, Rick Perry and Scott Walker, were similarly critical of Trump. The Republican National Committee also put its thumb on the scale, issuing a statement saying "there is no place in our party or our country for comments that disparage those who have served honorably."
Until now, Republicans have been largely cautious in their handling of Trump and his provocations.
While officials privately fretted about the damage he could do to the party, they are also worried about alienating voters drawn to his celebrity, brashness and willingness to take on establishment Republicans. He's emerged as one of the favorites early in a race that is bound to see shifts in the standing of many of the candidates.
Trump has made other eyebrow-raising comments since declaring his candidacy, most notably his assertion that Mexican immigrants are rapists and drug dealers. Many GOP candidates were slow and halting in their response to those comments, underscoring a continuing struggle to hit the right notes on immigration when they want to appeal to Hispanics without alienating traditional GOP voters.
But for a party that prides itself on its support for the military, Trump's comments about McCain were an easy opening. McCain, the 2008 GOP presidential nominee, spent more than five years as a prisoner of war, enduring torture and refusing release before fellow captives.
Democrats reminded voters about the tepid response to his earlier bombast.
Hillary Rodham Clinton, the Democratic front-runner, called McCain a genuine war hero and said it was shameful "that it took so long for most of his fellow Republican candidates to start standing up to him." Jim Webb, the former Virginia senator and Vietnam veteran, said Trump managed to offend Mexican-American military members twice.
Trump noted he got a standing ovation after his remarks to a religious conservative forum in Iowa, telling ABC's "This Week" that "nobody was insulted." But his comments about McCain drew a smattering of boos, his rivals received standing ovations, too, and when two of them repudiated Trump in their own remarks — South Carolina Sen. Lindsey Graham and former Texas Gov. Rick Perry — they got hearty applause.
To some Republicans, Trump's continued presence in the field will have a detrimental effect on other candidates.
"It's all Trump, all the time," said Matt Strawn, the former Iowa GOP chairman. For candidates still introducing to voters and trying to qualify for the party's first debate Aug. 6, Strawn said, "it is all but impossible for them to cut through the Trump noise." Although polls this early in a presidential contest are of dubious reliability, they are being used to determine who can come to the debate, and Trump appears likely to make the cut.
Pennsylvania GOP chairman Rob Gleason doesn't mind the fuss kicked up by Trump. He says it's drawing more attention to the Republican field.
"Now there's more people interested in what the Republican Party has to say," Gleason said. "It's all good. It keeps attention to politics, it really does."
Also looming over Trump's White House aspirations: the prospect he could run as a third-party candidate if he doesn't win the GOP nomination. Trump declined to rule that out when asked Saturday.
Echoing the concerns of many Republicans, GOP pollster Frank Luntz said Trump could siphon off enough votes as a third-party candidate to cost the party the White House.
"If you tell me Trump is running as an independent, I will tell you that the next president will be Hillary Clinton," said Luntz, who moderated the Iowa forum and asked Trump about McCain being a war hero.
Perry, one of the few veterans running for president, said Trump has demonstrated he has neither the character nor the temperament for the White House. "Over the top," he said on NBC's "Meet the Press." ''Really offensive." Bush, whose wife is from Mexico, took sharp offense at Trump's earlier comments as others hedged. After Trump's comments about McCain, the former Florida governor tweeted, "Enough with the slanderous attacks."
Trump pressed ahead Sunday with his critical remarks on McCain, who had no comment. He said the senator has been "all talk, no action" on looking after military veterans, and he complained that Americans who fought in wars without being taken prisoner get no attention. McCain stirred Trump's anger last week when he said Trump's comments about immigrants had "fired up the crazies" at a Phoenix rally.