A fierce debate is underway among centrist and left-leaning economists, taking place in newspaper op-eds, heated exchanges on Twitter, and even at the White House lectern. Unlike most internecine battles within a narrow intellectual tribe, this one will shape the future of the American economy and the political fortunes of the Biden administration.

The core question is whether the administration’s $1.9 trillion pandemic rescue plan is too big. Is action on that scale needed to contain the economic damage from the coronavirus and get the economy quickly on track to full health? Or is it far too big relative to the hole the economy’s in, thus setting the stage for a burst of inflation followed by a potential recession, as leading center-left economists including Larry Summers (the former Treasury secretary) and Olivier Blanchard (a former chief economist at the International Monetary Fund) have argued in recent days?

This clash of ideas is taking place at a crucial moment. With the Senate at a 50-50 partisan divide, a single Democratic senator who finds the arguments of Mr. Summers and Mr. Blanchard persuasive could require President Biden to trim his ambitions, with far-reaching consequences for his presidency and the economy.

The substance of the debate touches on important macroeconomic concepts like economic speed limits, the risks of deficits and the origins of inflation. But it is impossible to separate the substance from the personal history of those involved.

It has created stark divides among economic policy thinkers who for the most part know one another, have worked together in government, have spoken at the same think tank events, and share mostly similar political views.

Hanging over it all is the legacy of the Clinton-era Democratic policy establishment, and a continuing debate about past policy decisions.

What is in dispute?

President Biden’s pandemic aid plan includes direct spending for Covid testing and vaccine rollout, expanded unemployment insurance, money for schools and child care, and $1,400 payments to most Americans. It comes on the heels of a $900 billion bipartisan pandemic aid act enacted in December.

For weeks, policy veterans have been fretting among themselves over the scale of Mr. Biden’s proposal, in private emails and text chains. Mr. Summers made those concerns public with an op-ed in The Washington Post last week. Mr. Blanchard has backed him on Twitter, as has Jason Furman to some degree, chairman of the Council of Economic Advisers under President Barack Obama.

What is their argument?

As Mr. Summers wrote, it is a good idea to spend whatever it takes to contain the virus and enable the economy to recover quickly from its pandemic-induced downturn. Provisions that strengthen the safety net for those who are suffering are worthwhile.

The problem, he says, is that the plan’s total size reaches a scale that risks major future problems. In particular, the total money being proposed far exceeds most estimates of the “output gap.” (More on that below.) That implies that much of that spending will just slosh around the economy, causing prices to rise, potentially hindering the rest of Mr. Biden’s agenda and risking a new recession.

This isn’t a conventional argument between doctrinaire deficit hawks and doves, but something more subtle. In the past, Mr. Summers in particular has repeatedly called for larger budget deficits to help combat “secular stagnation,” in which major world economies are mired in slow growth, and he has supported large pandemic aid packages.

But Mr. Summers says any new spending package should pay out gradually over time and be devoted more substantially to long-term investments.

“There is nothing wrong with targeting $1.9 trillion, and I could support a much larger figure in total stimulus,” he wrote in a follow-up article. “But a substantial part of the program should be directed at promoting sustainable and inclusive economic growth for the remainder of the decade and beyond, not simply supporting incomes this year and next.”

What’s the output gap?

Imagine a world in which the American economy is cranking at its full potential. Pretty much everyone who wants to work is able to find a job. Every factory is at its complete capacity. The output gap is, simply, how far away the economy is from that ideal state.

A traditional approach to fiscal stimulus has been to estimate the size of that gap, apply some adjustments to account for the way federal spending circulates through the economy, and use that arithmetic to decide how big a stimulus action ought to be.

In theory, if the government pumps too much money into the economy, it is trying to generate activity over and above potential output, which is impossible to sustain for long. Workers might put in overtime, and a factory might run extra hours for a while, but eventually the workers want a breather, and the machines need to shut down for maintenance. If there is more money floating around in the economy than there is supply of goods and services, the result won’t be increased prosperity, but rather higher prices as people bid up the things they want to buy.

By that traditional thinking, Mr. Summers and other skeptics are on solid ground. The Congressional Budget Office is projecting an output gap for 2021 of only $420 billion, implying that $1.9 trillion in additional cash is much more than the economy needs to fill the gap. Even if you believe the C.B.O. is too pessimistic about America’s potential, we’re talking orders of magnitude of difference.

There are problems with this argument, though. For one, potential output is a theoretical concept, not something we can ever know with precision. In fact, there is a solid case to be made that technocrats have underestimated the economy’s true potential for years, given the absence of inflation in 2018 and 2019 despite a hot job market.

For another, it imagines the economy as a series of hydraulic tubes, in which a skilled engineer can push the right buttons to achieve a predictable outcome. In macroeconomics, especially in the era of a once-a-century pandemic, things might not be so simple.

How is the Biden administration responding?

Aggressively.

Treasury Secretary Janet Yellen and other top officials have taken to the airwaves in recent days to argue that their proposal is prudent and appropriately scaled.

Administration officials have described the plan as “bottom-up,” meaning it was devised by starting with specific problems facing Americans — a lack of income for those out of work, bottlenecks in vaccine delivery, a lack of funds for school reopening — and then ending with forecasts of the sums necessary to solve those problems.

Their argument is that the United States is in a do-whatever-it-takes moment, and that the most urgent goal is to try to ensure that the economy can fully reopen as quickly as possible while preventing potential lasting damage to families and businesses.

“I think that the idea now is that we have to hit back hard; we have to hit back strong if we’re going to finally put this dual crisis of the pandemic and the economic pain that it has engendered behind us,” Jared Bernstein, a member of the White House Council of Economic Advisers, said in a news briefing Friday.

They do not dismiss the possibility that there will be higher inflation down the road — but say it is a manageable risk.

Inflation is “a risk that we have to consider,” Ms. Yellen said on CNN’s “State of the Union” on Sunday, but “we have the tools to deal with that risk if it materializes” and “we have a huge economic challenge here and tremendous suffering in the country.”

“That’s the biggest risk,” she said.

In the logic that has prevailed within the administration and among other former officials who support the approach, it misses the point to theorize about output gaps and inflation risks. They say this relief should be thought of differently than traditional fiscal stimulus.

“Relief payments are life support,” wrote Austan Goolsbee, another former Obama adviser. “To avoid permanent damage, they need to last as long as the virus does. Without them, the chance of deterioration and irrevocable harm soars.”

So if this passes, is there really going to be a huge burst of inflation?

Maybe.

The economy is in uncharted territory. With potentially trillions of pandemic aid spending on the way — in addition to vast accumulated savings over the last year because of Americans’ pandemic-constrained spending and stimulus-boosted incomes — there is a lot of money poised to be spent.

And some things may reduce the supply of goods and services, like disruptions to global supply chains resulting from the pandemic and business closures.

Lots of money chasing finite supply is an Economics 101 recipe for surging prices.

But for the medium term, the more important question is whether any inflation surge would be a temporary not-so-harmful phenomenon or the start of something more lasting.

Why does that matter?

The Federal Reserve will be inclined to mostly ignore a one-time shock of post-pandemic inflation. Chair Jerome Powell said so in a news conference last month.

There is a possibility “that as the economy fully reopens, there’ll be a burst of spending because people will be enthusiastic that the pandemic is over,” Mr. Powell said. “We would see that as something likely to be transient and not to be very large.”

In that case, he said, “the way we would react is we’re going to be patient.”

It might even help rebalance the economy after years in which the United States has depended on low interest-rate policies from the Fed to keep growth afloat. Somewhat higher inflation would mean lower “real,” inflation-adjusted interest rates, and might gain the Fed some credibility that it will not permit inflation to be persistently too low. It could, plausibly, get back to above-zero interest rates sooner than it would otherwise, taking the air out of financial bubbles and giving it more room to combat the next downturn.

However, if surging prices were to create a vicious cycle of higher prices and higher wages, the Fed would be inclined to raise interest rates enough to try to break that cycle — potentially driving the economy into another recession in the process. That is the last thing that American workers need, let alone Democrats seeking to hold Congress in 2022 and the White House in 2024.

So is this part of a wider philosophical divide among Democratic economists?

There is no ideological chasm here.

But there is a deeper division than just the technical question of the output gap’s size or what the risks are of too much versus too little pandemic aid. Rather, the Biden approach represents a rejection of the technocratic bent within the Democratic Party that many on the left believe has been deeply damaging to the country.

President Bill Clinton and President Obama relied for economic advice on what might be called the Bob Rubin coaching tree. Mr. Rubin, who served as Treasury secretary in the 1990s, was a mentor to Mr. Summers, who was a mentor to Timothy Geithner, Mr. Obama’s first Treasury secretary, and so on.

The policymakers in this tradition view themselves as rigorous, careful and pragmatic. Many liberals view them as excessively moderate, too deferential to Wall Street and clueless about the political dynamics that could make for durable policies to help the working class.

The Biden administration includes many top officials from outside that tree, such as Ms. Yellen. And it is particularly seeking to correct what are seen as the mistakes of the early Obama administration, when Mr. Summers and Mr. Geithner were in top jobs.

The new administration sees this as a moment of profound crisis, a time when it must act on a scale commensurate with the problem. It is betting that if it solves the problem, its political fortunes will be better rather than worse, and it can always deal with inflation or other side effects if they come.

In a sense then, the debate over pandemic aid isn’t entirely about output gaps or risk trade-offs. It’s about which mode of policymaking ought to prevail in the Democratic Party.