Donald Trump’s tax and spending plans would explode the deficit, according to independent analyses, but tea party voters, the political movement born as a protest against government debt, are still willing to roll the dice with the billionaire businessman, saying he is the closest thing they have to a political home this year.

While demands to shrink the debt remain strong within the ranks, the activists said Mr. Trump’s appeal rests on a deeper disdain for Washington that they said has always been part of the movement’s DNA.

They also doubt the analysts who say Mr. Trump’s tax cuts will sink the nation trillions of dollars deeper into debt, with Sal Russo of Tea Party Express calling those reports misleading.

“He is not going to have deeply thought-out ideas,” Mr. Russo said. “I think when you support Trump, you are supporting someone who is an outsider, who is going to bring outsiders to bear to solve problems. He looks at things from a businessman’s perspective.”

The latest forecast from the Committee for a Responsible Federal Budget, a nonpartisan group, said Mr. Trump’s plan would add more than $5 trillion to the debt over the next decade while Mrs. Clinton’s plans would add a further $200 billion onto already-projected deficits.

It also said that Mrs. Clinton’s plans would push the national debt from 77 percent of gross domestic product to 86 percent and that the Trump plan would push it to 105 percent.

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Asked about those specific findings in the final debate, both candidates danced around the issue.

“Neither Clinton nor Trump is truly preparing the public for hard choices and compromises, which will make it all the more difficult for whoever wins the election to solve the problems,” Bob Bixby of the Concord Coalition, a nonpartisan group that advocates for eliminating deficits, said after the debate. “Instead of building a mandate for comprehensive reforms, they are building in unrealistic expectations among their hard-core followers. This only risks further public cynicism.”

Judson Phillips, the founder of Tea Party Nation, who has yet to back Mr. Trump, said he had hoped for more debate this year over runaway spending and the debt, which he called “the No. 1 national security threat.”

But he said he is not surprised that tea party voters have settled for Mr. Trump.

“One of the reasons that people have turned to Trump is simply because they are so angry,” Mr. Phillips said. “The Republican Party has been running for years on ‘We are the party of small government,’ and then they get into Washington and they are as much big spenders as Democrats are. And you can lie to people only so many times.”

The tea party rose out of the frustration with the growth of government under George W. Bush, who oversaw a $5 trillion increase in the debt, and then President Obama, who has presided over a further $10 trillion.

The movement is credited with helping Republicans take control of the House in 2010 and the Senate in 2014. But it has had less luck putting an imprint on presidential elections, where the electorate is much more diverse and larger.

Mr. Trump’s fiscal blueprint banks on generating an average of 3.5 percent economic growth per year — levels not seen since the tech boom of the 1990s — through a combination of lower taxes, less regulation and reshaped trade deals.

On the spending side of the ledger, Mr. Trump has promised to eliminate “waste, fraud and abuse” in nondefense discretionary programs, increase military spending and to leave the biggest drivers of government spending — Social Security and Medicare — untouched.

Budget hawks and economists say Mr. Trump’s projections are overly optimistic, and the CRFB said even if he hits his growth targets he will still add $1.5 trillion to the national debt. If growth stays at 2 percent, the debt would grow $5.3 trillion, the group said.

Jenny Beth Martin, head of Tea Party Patriots Citizens Fund PAC, though, doubted the findings and said she has confidence in Mr. Trump’s ability to deliver on his promises.

“My first question would be is have those economists been in a position to create jobs on their own?” Ms. Martin said. “The second thing I would say, it is certainly possible [to have 3.5 percent economic growth.] We are a country where things seem impossible and we make them possible. We put a man on the moon. Are you telling me we can’t balance the budget? We can’t grow the economy?”

She added, “I do think he will be better than Hillary Clinton.”