President Biden’s proposed $1.9 trillion pandemic rescue package includes money for many goals: expediting the rollout of coronavirus vaccines; reopening schools; expanding unemployment benefits; sending more cash payments to most Americans.

But when you skip the line-by-line details and look at the overall numbers, something striking becomes evident. The administration’s proposal, when combined with the $900 billion in pandemic aid agreed to in December, would amount to a bigger surge of spending, both in absolute terms and relative to the depth of the nation’s economic hole, than has been attempted in modern American history.

Mr. Biden’s proposal — or even more limited versions of it that appear to have a better shot of winning congressional approval — would pump enough money into the economy to, in effect, intentionally overheat it. Or at minimum it would push the limits of how fast the American economy can rev.

Supporters of aggressive stimulus aid view that as a positive thing, a means to finally correct the mistakes of the last recession and achieve a boom-time economy quickly, rather than muddle along with millions out of work for years.

Mark Zandi of Moody’s Analytics, whose work on the impact of fiscal stimulus President Biden has frequently cited, estimates that the United States currently has an “output gap” — a gap between actual activity and economic potential — of 4 percent to 5 percent of G.D.P., and that the Biden proposal would amount to 8 percent to 9 percent of this year’s G.D.P.

Even if scaled back somewhat to gain moderates’ support, the Biden plan implies enough fuel to get the economy burning hot.

“It’s better to err on the side of too much rather than too little,” Mr. Zandi said. “Interest rates are at zero, inflation is low, unemployment is high. You don’t need a textbook to know this is when you push on the fiscal accelerator. Let’s go.”

To skeptics, it would be a risky use of the power of the Treasury, with far-reaching implications for inflation, financial bubbles and the sustainability of the national debt.

“We’re already in uncharted territory,” said Douglas Holtz-Eakin, president of the American Action Forum and a former director of the Congressional Budget Office who has advised Republicans. He noted that fourth-quarter G.D.P. was only about $119 billion below its level of a year earlier: “Do we need another $1.9 trillion to deal with that problem? I have an arithmetic problem with where we are.”

Traditional fiscal policy to address a recession goes something like this. First make your best projection of how the economy will perform in the months ahead. Then make your best guess at how much smaller that is compared with the economy’s potential if healthy — for example, the value of G.D.P. if everyone who wanted a job was working and factories were running at full capacity.

At that point, try to analyze the “fiscal multipliers” of policies under consideration: how much economic activity each dollar of spending is likely to trigger. Then size your fiscal stimulus package accordingly, essentially using federal dollars to replace the economic activity that has evaporated because of the recession.

In practice, of course, it’s never that simple. It includes a lot of estimates and projections, and congressional politics will ultimately determine the size and content of stimulus legislation. Constrained by Congress, President Barack Obama’s signature fiscal stimulus program, enacted in early 2009, was a poor match for the economic crisis at hand. It pumped an average of $240 billion into the economy each of its first three years, at a time the “output gap” approached $1 trillion per year.

The approach of both parties in fighting the pandemic-induced downturn has focused less on the big picture. It has been more about assembling provisions to help individuals and businesses weather the crisis, whatever the price tag. Under that approach, large bipartisan majorities enacted the $2 trillion CARES Act in the spring and several smaller provisions, including the $900 billion package a month ago.

These efforts are less fiscal stimulus in the traditional sense — using government money to replace missing demand in the economy — and more an effort to directly alleviate the problems the pandemic has caused.

“This package is sized not simply to fill the hole,” said Wendy Edelberg, director of the Hamilton Project at the Brookings Institution. “It’s trying to do somewhat different things. A lot of people and businesses are desperately hurting right now, so this money is relief aimed at those people, and in order to be really confident you’re reaching them all, you need to send a lot of money.”

But that doesn’t change the fact that the aggregate money the government is pumping out adds up to more than the missing economic activity, which could have meaningful consequences for the years ahead. And that is before accounting for other expected proposals from the Biden administration, such as large-scale funding of new infrastructure.

“There are pros and cons,” she said. “Running the economy hot might be a good thing, but there also might be a painful adjustment with a period of slow growth on the other side of the mountain.”

In an economy running hot, employers face shortages of workers and must bid up their wages to attract staff. This, along with potential shortages of various commodities, can, in theory, fuel a vicious cycle of rising prices.

For the last 13 years, arguably longer, the United States has had the opposite problem. Large numbers of Americans of prime working age — 25 to 54 — have been either unemployed or outside the labor force altogether. Wage growth has been weak most of that time, and inflation persistently below the levels the Federal Reserve aims for.

Some argue that estimates of potential output by the C.B.O. and private economists are too pessimistic — that Americans should dare to dream bigger. “We don’t really know what the G.D.P. output gap truly is,” said Mark Paul, an economist at New College of Florida. “Economists for decades have erred and been too cautious, thinking that full production is significantly lower than it actually is. We’ve been consistently running a cold economy, creating massive problems for social cohesion.”

In a paper published in December, he said a pandemic aid package of more than $3 trillion would be justified based on the scale of job losses that have been endured. The output gap looks worse based on employment than it does when you look at G.D.P., in part because job losses have disproportionately occurred in sectors that generate relatively low economic output per worker, such as restaurants.

Still, the scale of the pandemic aid already in train helps explain why Mr. Biden faces a tricky road toward finding a Senate majority for the next bill, even among Republicans who are not dead set against stimulus spending conceptually.

“It’s hard for me to see, when we just passed $900 billion of assistance, why we would have a package that big,” Senator Susan Collins, the Maine Republican, said recently. “Maybe a couple of months from now, the needs will be evident and we will need to do something significant, but I’m not seeing it now.”

A key case for going large revolves around risk management. With the economy mired in a cycle of weak labor markets and low inflation, a little overheating might be welcome. If, for example, the Federal Reserve needed to raise interest rates down the road to keep inflation from taking off, it could be a positive thing for creating a more balanced economy less reliant on monetary policy and booming asset prices.

Jerome Powell, the Federal Reserve chair, has said that ensuring the long-term productive capacity of the economy is a more urgent priority than tamping down inflation.

“I’m much more worried about falling short of a complete recovery, and losing people’s careers and lives that they built, because they don’t get back to work in time,” Mr. Powell said in a news conference Wednesday. “I’m more concerned about that than about the possibility which exists of higher inflation. Frankly, we welcome slightly higher inflation.”

Put differently: It’s hard to worry too much about getting burned after a decade-long winter out in the cold.