Washington (CNN) Donald Trump is testing just how far he can push his unconventional campaign without wrecking it.

The Republican nominee shattered traditional political boundaries Tuesday when he told The Washington Post he isn't backing House Speaker Paul Ryan or Sen. John McCain as they face primary challenges. The two leading Republicans seemingly angered Trump with their denunciation of his criticism of the family of a slain Muslim US soldier.

Trump's comments -- delivered to a newspaper he's banned from attending his events since mid-June -- capped a bizarre day on the campaign trail that also included asking for a crying baby to be removed from a rally and causing a stir over Purple Heart recipients.

In his interview with the Post, Trump criticized Ryan, saying, "We need very strong leadership."

"We need very, very strong leadership," Trump said. "And I'm just not quite there yet. I'm not quite there yet."

Trump's phrasing -- "I'm not quite there yet" -- echoes comments Ryan made to CNN's Jake Tapper in May when he said he wasn't yet ready to back his party's standard-bearer. Zach Roday, a Ryan campaign spokesman, said the speaker hasn't asked for Trump's endorsement and is "confident in a victory next week regardless."

A source close to Republican National Committee chairman Reince Priebus told CNN he was incredibly upset with Trump for refusing to endorse Ryan in his primary.

This source noted that for Priebus it is "personal" because he and Ryan -- both from Wisconsin -- are as close as family and Priebus was the chairman of Ryan's first congressional race.

"He takes this very personally," said the source, especially since "he has taken on a lot of water" for Trump.

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Trump's comments come as he is under the most severe bipartisan fire of his campaign following his criticism of Khizr and Ghazala Khan, whose son Humayun Khan, died in Iraq in 2004. The Khans delivered one of the most powerful appearances at last week's Democratic National Convention, where Khizr said Trump has "sacrificed nothing and no one."

Trump's response

Trump responded by criticizing Ghazala Khan's silence, suggesting she wasn't allowed to speak because of her religion and saying he made plenty of sacrifices for his business.

The Republican nominee has struggled to recover from the episode as easily as he has from previous controversies. A knowledgeable GOP source told CNN some of Trump's campaign staff -- even campaign chairman Paul Manafort -- are incredibly frustrated with the candidate. Some staffers "feel like they are wasting their time" because Trump has veered off message so much since the Democratic convention.

Trump spokesman Jason Miller rejected suggestions that Manafort is "mailing it in" as "completely erroneous." The campaign "just finished up our strongest month of fundraising to date, we're adding talented and experienced staffers on a daily basis and Mr. Trump's turning out bigger, more enthusiastic crowds than Hillary Clinton ever could."

Still, Trump's challenge became clear in a series of strange moments Tuesday.

At a rally in family-friendly suburban Northern Virginia, Trump reversed the stereotype of baby-kissing politicians when he called for a wailing infant to be ejected -- spurring laughter after initially saying how much he loved babies. He also caused a stir when a military veteran gave Trump a Purple Heart, prompting Trump to say he "always wanted a Purple Heart" and this was "much easier" than serving in combat.

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"The notion that he would attack a Gold Star family that made such extraordinary sacrifices on behalf of our country, the fact that he doesn't appear to have basic knowledge of critical issues in Europe, the Middle East, in Asia, means that he's woefully unprepared to do this job," Obama said.

In an interview with Washington's WJLA-TV, Trump said it's Obama who is "unfit" for the Oval Office.

"He's a terrible president," Trump said. "He'll probably go down as the worst president in the history of our country. He's been a total disaster."

And as much of the political world looks on in horror, Trump's supporters remain loyal, cheering him on at Tuesday's rally in Ashburn, Virginia.

Alienation from the party

But his alienation from the rest of the party establishment only seemed to grow.

Maria Comella, a longtime aide to New Jersey Gov. Chris Christie, told CNN's Jamie Gangel Tuesday she plans to vote for Hillary Clinton , saying Republicans are "at a moment where silence isn't an option."

"Donald Trump has been a demagogue this whole time, preying on people's anxieties with loose information and salacious rhetoric, drumming up fear and hatred of the 'other,'" Comella said.

"Instead of trying anything remotely like unifying the country, we have a nominee who would rather pick fights because he views it as positive news coverage," she said. "It may make him media savvy, but it doesn't make him qualified or ready to be president."

Meg Whitman, the Hewlett Packard chief executive who ran in 2010 for governor of California as a Republican, also said Tuesday she would support Clinton.

In a statement, she blasted Trump's "demagoguery" and said his positions on immigration, the economy and foreign policy "have made it abundantly clear that he lacks both the policy depth and sound judgment required as President."

"It is clear to me that Secretary Clinton's temperament, global experience and commitment to America's bedrock national values make her the far better choice in 2016 for President of the United States," she said. "I urge all Republicans to reject Donald Trump this November."

The comments follow Sally Bradshaw, a senior Jeb Bush advisor, who told Gangel Monday she had quit the party and would vote for Clinton if Florida was close.

"This is a time when country has to take priority over political parties. Donald Trump cannot be elected president," Bradshaw said.

Hanna is not running for re-election so he has less at stake than other Republicans. But he's not the only Republican moving away from Trump.

Top party leaders including Ryan and Senate Majority Leader Mitch McConnell are feeling the pressure. Though they have criticized Trump's feud with the soldier's family, they have yet to walk back tepid endorsements of Trump.

McCain went further than virtually any of his colleagues in a statement on Monday.

"While our Party has bestowed upon him the nomination, it is not accompanied by unfettered license to defame those who are the best among us," McCain said. "I cannot emphasize enough how deeply I disagree with Mr. Trump's statement. I hope Americans understand that the remarks do not represent the views of our Republican Party, its officers, or candidates."

But even the Arizona senator, facing a re-election race in which he needs both pro-Trump and anti-Trump voters, did not explicitly call on Republicans to dump their nominee.

That point could yet come, should Clinton's seven-point convention bounce solidify into a sustained polling lead.

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During his news conference, Obama expanded on an emerging Democratic strategy to convince die-hard Republicans not to put a cross next to Trump's name in November, even if they vote the rest of the GOP ticket.

'Why are you still endorsing him?'

"If you are repeatedly having to say in very strong terms that what he has said is unacceptable, why are you still endorsing him?" Obama asked. "This isn't a situation where you have an episodic gaffe."

He went on: "There has to be a point in which you say this is not somebody I can support for president of the United States, even if he purports to be a member of my party. ...There has to come a point at which you say enough."

In another example of a scattershot campaign, Trump's son, Eric, was drawn into a discussion about workplace behavior following the resignation of Fox News chief Roger Ailes over sexual harassment allegations.

He told CBS' Charlie Rose that said his sister Ivanka was "strong" and "powerful" and would never allow herself to be sexually harassed by her boss

The comment drew a one-word tweet from Fox News host Megyn Kelly: "Sigh."

Still despite the gathering chaos around Trump, lingering questions still surround his campaign and those who criticize him.

He is so unorthodox that it is sometimes tough for those caught up in the maelstrom to judge what is happening against a credible political scale. His antics often beg the question of whether Trump has so skewed campaign logic that he has tapped into a connection with voters that normal politicians don't even recognize. That makes it far too early to write him off.

But equally, it's possible America is currently watching the meltdown of the billionaire's campaign. Perhaps the most unorthodox, unpredictable candidate ever has hit limits of political convention that even he can't trump?

American political sages are not alone in trying to figure out the riotous election -- the world is watching too.

Singapore Prime Minister Lee Hsien Loong was cast in the role of puzzled foreigner as he stood alongside Obama in the White House.

Lee noted that often, after volatile election campaigns, a cooler atmosphere prevails and the ship of state "does not turn completely upside down" and putting his faith in the system of checks and balances.

"It is not so easy to do things, but it is not so easy to completely mess things up," he said.