He has spent the past year mocking President Obama’s debt buildup, but Donald Trump let the country in on a secret last week: He would rack up even more red ink before all is said and done.

Mr. Trump, in part of an interview with CNBC that is getting less attention than his other food-fight-style comments, said that with interest rates so low, “this is the time to borrow” in order to pay for more than $500 billion in infrastructure he wants to build.

Analysts and Republican activists said Mr. Trump is making a mistake, both economically and politically, threatening one of the few areas of agreement within the party, including among moderates and tea partyers, that new spending should be offset, not tacked onto the debt for future generations to cover.

“I’ve been a Trump guy from the beginning, but I’ve got to tell you, the debt comments bother me,” said Ken Crow, a tea party leader and Trump supporter in Iowa. “I’m furious, to be honest with you.”

While short on details, Mr. Trump has said he would like to spend at least $500 billion on infrastructure, twice as much as Democratic opponent Hillary Clinton. He also proposes to raise spending for the Defense and Veterans Affairs departments even as he cuts tax rates, sapping revenue in the near term.

Asked how he would fund his plan, the billionaire businessman told CNBC that he would go into debt.

“The interest rates are so low, I mean the numbers are so low, that yes, this is a time to borrow, and to borrow long term, so we can have the money and rebuild our infrastructure,” he told the network in a long interview last week. “We can have the money. We have things; we have no choice.”

He announced his support for debt after months of attacks on the deficits that have accumulated during Mr. Obama’s tenure. The president took office with total government debt at $10.6 trillion, and the figure as of Monday was $19.4 trillion. Debt held by the public — a more precise measure of the government’s obligations to creditors — has more than doubled, from $6.3 trillion to $14 trillion.

Mr. Trump’s campaign didn’t respond to a request for comment on his new affinity for government debt, but analysts said his read of economics is strained.

Marc Goldwein, senior vice president at the watchdog Committee for a Responsible Federal Budget, said Mr. Trump’s low-interest theory matches a call from the political left, which says if government borrows and pumps the money into productive investments, the economic boost will more than cover the eventual higher interest payments on the debt.

“That’s all fine and good in theory. The problem is when you turn a theory into practice,” Mr. Goldwein said.

In this case, the U.S. already has a massive load and little prospect of paying it down. That means the new debt would be rolled over at some point, at interest rates higher than today’s low rates, skewing the economics. Besides, Mr. Goldwein said, there is scant evidence that infrastructure spending can pay for itself if done as Mr. Trump wants.

The Congressional Budget Office recently published an analysis of several investment scenarios, including spending some $500 on short- and long-term projects, and said it could boost the economy — but only if it is offset with cuts elsewhere in the budget. If the money is tacked onto the deficit, it will sap the economy and leave an even bigger hole in the budget, the CBO said.

Mr. Trump’s new stance on debt contrasts with that of his running mate, Indiana Gov. Mike Pence, who has made cutting spending and reducing deficits a hallmark of his public career. While in Congress, Mr. Pence opposed President George W. Bush’s $400 billion prescription drug expansion of Medicare and led a failed effort to try to force the administration to pay for Hurricane Katrina spending with offsets elsewhere in the budget.

Mr. Trump has praised Mr. Pence’s debt-fighting on the campaign trail but explained to CNBC that low interest rates are too much of an enticement to pass up.

“Normally, you would say you want to reduce your debt, and I like to reduce debt too, as much as anybody. The problem is you have a military problem, you have an infrastructure problem,” he said. “And also, the asset is, your rates are so low. What’s going to happen when the rates eventually are going to go up and you can’t borrow, you absolutely can’t borrow because it’s too expensive? It would destroy our balance sheet.”

Douglas Holtz-Eakin, a former director of the CBO who is now president of the American Action Forum, said spending might boost the economy if it’s in recession, but the U.S. is close to full employment, so there is not a lot to reduce. And the federal government will eventually have to pay off the debts.

“Borrowing is the same as having taxes higher in the future,” he said.

He also dismissed Mr. Trump’s claim that he would be able to renegotiate U.S. debt, forcing America’s creditors to take pennies on the dollar. Mr. Holtz-Eakin said that even if Mr. Trump is able to do so as president, it would set a bad standard and hurt the U.S. in other economic dealings.

Economics aside, Mr. Trump’s call for more debt appears to be bad politics. As he still struggles to unify Republicans, his plan has deepened the rift.

“Trump’s comment is simply stunning,” said Judson Phillips, who founded Tea Party Nation. “One of the reasons I refuse to support Trump is comments like he has on the debt. He clearly has no clue how to manage the economy and will lead America into yet another great depression.”

Mr. Crow, the Iowa tea party leader who is still backing the Republican nominee, said he was on a call with Mr. Trump before his state’s caucuses and asked the candidate about debt. At the time, Mr. Trump said the country couldn’t afford more red ink.

Mr. Crow said Mr. Trump’s about-face suggests he is pandering like other politicians, surrendering the qualities that made him a standout during the Republican primary race.

“Trump wants to build roads and bridges, and the Democrats want to give it to unions. What’s the difference? Our money’s being wasted,” Mr. Crow said. “I think he’s just capitulating to garner votes. I think he jumped into the ‘I’m a politician now’ mode, and that’s not what made him popular.”

Debbie Dooley, one of those involved in organizing the first tea party protests in 2009, said she wants to see the debt cut, but she is backing Mr. Trump because of his stances on immigration and trade.

“I look at the fact that Ronald Reagan increased the debt. I would prefer the debt be cut, but that hasn’t happened,” she said.

Despite Mr. Trump’s plans to borrow, Ms. Dooley predicted that he would fix economic problems.

“Mr. Trump is looking out for the best interests of Main Street, and I have no doubt he will cut the deficit and he will bring government spending under control,” she said.

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