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WASHINGTON – Donald Trump’s tweet on Tuesday dangling the idea of an independent run for president sent a clear warning to the Republican establishment: Attack at your own peril.

After 24 hours of withering criticism from the likes of Dick Cheney, Mitt Romney, Paul Ryan, Mitch McConnell and virtually every fellow GOP presidential hopeful — not to mention Democrats and the mayors of Philadelphia and London — Trump is defiantly standing by his proposal to ban Muslims from entering the United States. And he upped the ante by tweeting a new USA Today/Suffolk University poll that shows 68% of the 2016 Republican front-runner’s supporters would ditch the GOP and stick with him if he launched an independent campaign for the presidency.

Such a decision would almost surely rob Republicans of an opportunity to take back the White House in 2016. So Trump is bringing a deal-maker’s understanding of brinksmanship to the campaign trail: No matter how thoroughly Republicans trash him, he won’t change course because he knows the party needs him as much as or more than he needs it.

It was hardly as if party officials needed a reminder.

Even as leading Republicans lambasted Trump’s proposal to ban Muslims from entering the United States, most of the party’s top officials wouldn’t touch what Trump’s position means within the context of the future of the GOP.

Ryan insisted that “this is not conservatism” but still said he’d back the Republican nominee.

Republican National Committee Chairman Reince Priebus told the Washington Examiner he disagrees with Trump, but, pressed on how Trump’s proposal could hurt the party, he said: “That’s as far as I’m going to go.”

Even former Florida Gov. Jeb Bush wouldn’t backtrack from his pledge to support whoever wins the GOP nominating process if that happens to Trump, saying only, “Look, he’s not going to be the nominee.”

As for a Trump independent run, Bush tweeted that perhaps the real estate mogul had “negotiated a deal with his buddy” Hillary Clinton.

“Continuing this path would put her in the White House,” Bush tweeted.

Bush is likely right — but the outcome he warned about is just as much of a threat to the rest of the Republican Party as it is to Trump himself, and Trump has shown little fear of self-immolation.

On Tuesday, Trump defiantly tweeted, “Wow, what a day. So many foolish people that refuse to acknowledge the tremendous danger and uncertainty of certain people coming into U.S.”

Even Trump’s most outspoken critics can’t deny his command of the presidential race.

“You know how you make America great again? Tell Donald Trump to go to hell,” South Carolina Sen. Lindsey Graham said on CNN’s “New Day” on Tuesday.

Agreeing with Trump, or disagreeing with Trump, has been a full-time occupation for high-ranking Republicans since his campaign released its statement proposing the Muslim ban at 4:15 p.m. Monday.

The episode over Trump’s call for a ban on Muslims entering the United States has provoked a more severe backlash than Trump has faced before — even when he questioned the war-hero status of Arizona Sen. John McCain, a former prisoner of war and 2008 Republican presidential nominee.

Still, it’s also just the latest in a long string of controversies Trump has stirred — many with lasting effects on the presidential race.

First, Trump seizes on something — a fear of terrorism, in this case — and proposes a plan undeniably bolder than his opponents have, forcing questions on broader, often more fundamental questions than candidates can address through the comfort of their talking points.

Then the GOP field scrambles to react — and no matter how harsh Trump critics like Bush and Graham are, it never seems to dent the front-runner’s poll numbers.

All the while, the donor class and operatives running well-financed super PACs are failing to agree on — or even identify — any strategy to ultimately take Trump down.

It’s Trump’s modus operandi.

Early on, it was his attack on undocumented immigrants from Mexico — and his repeated insistence that he’d build a wall and Mexico would pay for it — that brought the issue of immigration to the forefront.

More than that, it left would-be insurgent candidates like Wisconsin Gov. Scott Walker and experienced hands like former Texas Gov. Rick Perry grasping for ways to sound tougher than Trump — forcing them out of their comfort zones and turning their campaigns too off-course to correct.

Now, the stakes are higher.

Weekly Standard editor Bill Kristol said that he’s “come to loathe” Trump because he’s “soiling the robe of conservatism and dragging it through the dust.”

But he also asked a question: “Other GOP candidates will denounce this. Will they also say they couldn’t support him if somehow he becomes nominee?”

So far, the answer has been no.

Trump has controlled the debate, but soon he’ll have to turn his attention to winning primaries and caucuses — a job perhaps made more difficult when early voting state GOP chairs lashed out at his latest proposal.

“As a conservative who truly cares about religious liberty, Donald Trump’s bad idea and rhetoric send a shiver down my spine,” South Carolina GOP chairman Matt Moore tweeted.

New Hampshire GOP chairwoman Jennifer Horn called Trump’s position “un-Republican.”

And Iowa Republican chairman Jeff Kaufmann rebuked Trump by tweeting, “I’m here to reiterate that our founding principles are stronger than political cynicism.”

None of the three, though, called on Trump to drop out — or denounced his candidacy.

That makes the grumbling — though louder this time — more of what Trump has already seen: A Republican establishment that might not like him, but can’t disavow him because it certainly hasn’t found a way to beat him. Trump’s continued flirtation with an independent bid has become a recurrent campaign theme — despite the party loyalty pledge he signed in September — and one that will clearly haunt the GOP as the primary season begins.

By Eric Bradner, CNN