"This is about math, not mystery and magic," said Mr. Simpson, who was a chairman of President Barack Obama's bipartisan commission on the federal debt in 2010. "It's madness to think that you can have a tax cut without some reduction in spending or some increase in revenue."

Some Republicans are rallying around the idea that less taxation is more important than less debt, just as they did during the Republican presidencies of Ronald Reagan and George W. Bush. That shift is a break with the die-hard hawks of the anti-deficit industrial complex, who have long warned of calamitous consequences to the American economy.

But when Republicans take charge, their fiscal rectitude sometimes starts to waver. The broad Republican support this week for President Trump 's plan to sharply reduce taxes suggests that those who hang on to austere concerns about debt will now be facing former allies who want to chase economic growth.

From an office high above Manhattan, the billionaire Peter G. Peterson has warned for years that the federal government is borrowing too much money. So have other Republican grandees, like former Senator Alan K. Simpson, who made dire predictions about the federal debt in a 2010 report. Republicans in Congress have been eager to sing from the same hymnal so long as a Democrat was in the White House.

Mr. Trump's proposal, while short on details, calls for cutting taxes on corporations and individuals, including reducing the corporate tax rate from 35 percent to 15 percent and doubling the size of the standard deduction for individuals. Analysts estimated that it could add as much as $7 trillion over a decade to the federal debt, depending on what Congress eventually packs into a tax bill.

That is particularly notable because the debt has already increased sharply over the last decade, growing from 34.8 percent of the nation's annual economic output at the end of 2006 to 76.5 percent at the end of 2016. Prominent figures like Janet L. Yellen, the chairwoman of the Federal Reserve and a Democrat, have urged lawmakers to curb that growth.

The prospect that the debt might balloon again instead is stirring anxieties within a range of well-financed groups that have long regarded Republicans as their natural allies.

"Right now, we are all about trying to figure out how to offset the cost of this framework and coming up with pro-growth tax reform ideas that won't worsen our really dire fiscal situation," said Maya MacGuineas, president of the nonpartisan Committee for a Responsible Federal Budget. "If the president pursues this proposal of seeing through the largest-ever tax cut rather than reform, he will also be the president who oversees the largest expansion of our country's debt — and that's probably not the legacy he's looking for."

Ms. MacGuineas said that her group had already started pulling together specific proposals to make the tax legislation less costly. The White House plan, for example, has thus far only made passing reference to proposals for closing loopholes and broadening the tax base, she said.

"It will be all hands on deck to try to come up with ideas," Ms. MacGuineas said.

Mr. Peterson created the Peterson Foundation in 2008, with an endowment of $1 billion, to raise public awareness of what he saw as an alarming increase in federal borrowing. The federal debt increased sharply during the early years of the Obama administration, largely because of programs that automatically disburse more money during economic downturns. When unemployment increases, so does federal spending on unemployment benefits.

Michael A. Peterson, the chief executive of the foundation and the son of its founder, warned lawmakers against forgetting that the nation is already deeply in debt.

"Reforming taxes in a way that worsens our fiscal condition is counterproductive because adding to our national debt hurts economic growth," he said in a statement Wednesday. "Tax changes that increase the deficit would harm the economy by raising interest costs, reducing wages and crowding out public and private investments in our future."

Conservative lawmakers, advised by conservative economists, once regarded government debt as a public health problem. The government is borrowing money that might otherwise be available to private businesses, which is bad for economic growth. The money must be repaid eventually, which requires higher taxes, which is also bad for economic growth. And higher debt leaves less room for government borrowing during a genuine emergency.

But Reagan, advised by economists like Milton Friedman, argued that taxation was a more important economic problem, and Republicans began to prioritize tax cuts.

This was, at the least, very good politics. President George H. W. Bush was not re-elected in 1992 in part because he did not join the revolution. He continued to advocate fiscal rectitude, famously agreeing to raise taxes because he wanted to reduce the federal debt. His son did not repeat that mistake during his presidency, and passed a tax cut.

The nation's financial situation was markedly different in 2001. The government was running a hefty annual surplus; it was actually on course to pay off its debts completely.

Democrats have been quick to accuse Republicans of ideological inconsistency. "The Republican plan is just steeped in hypocrisy," Senator Chuck Schumer of New York, the minority leader, said Thursday.

"For the last eight years, all we heard from our Republican colleagues was that Obama was raising the deficit, and we need to cut programs that benefit the poor and middle class," Mr. Schumer said. "All of a sudden, now, with a Republican president and a proposed tax cut for the wealthy, we're hearing from the other side of the aisle, 'Deficits don't matter.'"

Others still hold the view that deficits matter. Josh Gordon, the policy director of the Concord Coalition, another group that advocates fiscal discipline, said it was heartening that Speaker Paul D. Ryan and Senator Mitch McConnell, the majority leader, have expressed a commitment to changes that are "revenue neutral."

Representative Peter Roskam, the Illinois Republican who is chairman of the Tax Policy Subcommittee of the Ways and Means Committee, warned that his party should resist taking the easy route and passing temporary tax cuts in favor of making deeper changes to the tax code.

"The best thing to do is to create a tax policy that's permanent, and permanent means paid for," Mr. Roskam told MSNBC on Wednesday. "So that's the new fault line that is developing."

But some Republicans see an important difference between deficits caused by more spending and deficits caused by tax cuts. They insist that tax cuts will encourage economic growth sufficient to compensate for lower rates. The government will get a smaller piece of a larger pie.

Senator Jeff Flake, Republican of Arizona, said that he was committed to balancing the federal budget and that tax cuts could help achieve that goal. "I'm a supply-sider. I recognize the dynamic value of the nature of some tax cuts," Mr. Flake said. "Not all tax cuts are created equally. Corporate tax cuts should be very stimulative."

Representative Dave Brat, Republican of Virginia, who spent most of his career as an economics professor, said, "You've got to come clean with people that this is not optimal, but tax cuts are a way to drive productivity." The pain of a short-term increase to deficits, he said, was pain worth enduring for the sake of growth.

"The one thing you make an exception for is tax cuts."