The three Republicans challenging President Donald Trump for their party's nomination have a problem, which is that Trump's approval rating among GOP voters is steadfastly over 90 percent.

Former Gov. Bill Weld of Massachusetts, former Rep. Joe Walsh of Illinois, and former governor and congressman Mark Sanford of South Carolina are each running because they think the president is unfit.

But most of Trump supporters don't care. For them, the Republican Party was merely a vessel to get their man in power, where he would unapologetically savage their enemies.

At Business Insider's GOP debate last week, both Weld and Walsh admitted that they originally found Trump's style of anti-political correctness appealing.

Anti-Trump dissidents might be better off forming their own party, one which represents the erstwhile Republican values that were so soundly rejected by the GOP electorate in 2016.

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The three Republicans challenging President Donald Trump for their party's nomination have a problem, and they need to make a decision what to do about it.

The issue: Trump's approval rating among GOP voters is steadfastly over 90%. That leaves little appetite for an alternative among the only people whose opinion matters on this particular issue.

Former Gov. Bill Weld of Massachusetts, former Rep. Joe Walsh of Illinois, and former governor and congressman Mark Sanford of South Carolina are each running because they think the president is unfit for office, that his bouts of Twitter rage are eroding Americans' respect of the presidency, and that his "us and them" worldview is hateful.

Read more: GOP challengers Bill Weld and Joe Walsh slam Trump on trade war with China

The three GOP challengers also say Trump has betrayed the party's long-held principles of free market capitalism, maintenance of a robust foreign policy through international alliances, and an openness to immigrants as a vital part of America.

But most of Trump supporters don't seem to care about those principles. For them, the Republican Party was merely a vessel to get their man in power, where he would unapologetically savage their enemies (the liberal elites, the media, immigrants) and enact a right-wing populist agenda. If Trump started his own new political party tomorrow, his base would almost surely follow suit.

That begs the question: What exactly are Weld, Walsh, and Sanford fighting for?

Read more: GOP primary challenger Joe Walsh says he's 'a big gun guy' and that 'the numbers' on gun violence have been good the past few decades

The old Republican guard

Weld represents the socially liberal "Rockefeller Republican" brand — named for former New York governor and Vice President Nelson Rockefeller — which was mostly comprised of Northeast lawmakers who were ahead of the curve on issues like gay rights, but who also maintained a strict fiscal conservatism. That brand, however, has barely existed since the George W. Bush administration — which brought a style of big government "compassionate conservatism" to the forefront of the party.

Walsh and Sanford both come from the Tea Party, the previous surge of right-wing populism that had its biggest moments in the 2010 and 2012 congressional elections. But Walsh only served one term before pivoting to a career as a conservative radio talk show host, and Sanford lost his House seat in 2018 — in no small part because of his opposition to Trump.

The lesson was not lost on Sanford's Republican congressional colleagues, and for good reason. Trump is far more popular than they are.

As for old Republican tentpole issues like fiscal conservatism and balanced budgets and cutting deficits, no less a conservative authority than Rush Limbaugh admitted on his show this past June that "nobody is a fiscal conservative anymore. All this talk about concern for the deficit and the budget has been bogus for as long as it's been around."

Trump's GOP challengers each represent a certain Republican archetype that barely exists anymore. But they find common cause in decrying Trump's rhetoric — which now defines their party more than any economic policy.

The anger and offensiveness is the point

At Business Insider's GOP debate last week, both Weld and Walsh admitted that they originally found Trump's style of anti-political correctness appealing.

Walsh — who had previously been a vociferous Trump supporter — said, "I've been in the business of trying to break down political correctness for years because I want honest dialogue" and added that he thinks Americans have become "way too sensitive" on controversial issues like race relations.

Read more: Here is the full transcript of Business Insider's Republican primary debate between Joe Walsh and Bill Weld

Even the eloquent and effortlessly congenial Weld admitted during the debate that he had found Trump "appealing" as a candidate because of how "how un-politically correct" Trump was.

In this sense, Trump's challengers are able to empathize with his supporters.

But the question is, do any of them truly see any remaining semblance of the party they once knew and loved? Do they believe the GOP will return to its former self once Trump leaves office?

If they were to answer anything but "no," they'd need to show their work.

Read more: Trump's 2020 Republican challengers set a tone: It's not about electing someone else, it's about not electing Trump

Given the relative ease with which Trump took over the party in 2016, and the overwhelming and sturdy support of the his base, there's no reason to believe Republicans will reject Trump — and the force of his personality is likely to be endemic to the conservative movement for years to come.

What the Never Trumpers also must reckon with is what comes next if Trump loses reelection in 2020. Because if anger is baked into the Trump brand, it's unlikely that such a visceral emotion simply dissolves from the Republican Party just because the boss has left the building.

That's why Republican anti-Trump dissidents would be better off forming their own party, one which represents the erstwhile Republican values that were so soundly rejected by the GOP electorate in 2016.