WASHINGTON — Presidents who find themselves digging out of recessions have long heeded the warnings of inflation-obsessed economists, who fear that acting aggressively to stimulate a struggling economy will bring a return of the monstrous price increases that plagued the nation in the 1970s.

Now, as President Biden presses ahead with plans for a $1.9 trillion stimulus package, he and his top economic advisers are brushing those warnings aside, as is the Federal Reserve under Chair Jerome H. Powell.

After years of dire inflation predictions that failed to pan out, the people who run fiscal and monetary policy in Washington have decided the risk of “overheating” the economy is much lower than the risk of failing to heat it up enough.

Democrats in the House plan to spend this week finalizing Mr. Biden’s plan to pump nearly $2 trillion into the economy, including direct checks to Americans and more generous unemployment benefits, with the aim of holding a floor vote as early as next week. The Senate is expected to quickly take up the proposal as soon as it clears the House, in the hopes of sending a final bill to Mr. Biden’s desk early next month. Fed officials have signaled that they plan to keep holding rates near zero and buying government-backed debt at a brisk clip to stoke growth.

The Fed and the administration are staying the course despite a growing outcry from some economists across the political spectrum, including Lawrence Summers, a former Treasury secretary and top adviser in the Clinton and Obama administrations, who say Mr. Biden’s plans could stir up a whirlwind of rising prices.

No one better embodies the sudden break from decades of worry over inflation — in Washington and elite circles of economics — than Janet L. Yellen, the former Federal Reserve chair and current Treasury secretary. Ms. Yellen spent the bulk of her career fighting in a war against inflation that economists have been waging for more than a half century. But at a time when the American economy remains 10 million jobs short of its pre-pandemic levels, and millions of people face hunger and eviction, she appears to be ready to move on.

“I have spent many years studying inflation and worrying about inflation,” Ms. Yellen told CNN earlier this month. “But we face a huge economic challenge here and tremendous suffering in the country. We have got to address that. That’s the biggest risk.”

In the guarded language of a Fed chair, Mr. Powell used a speech last week to push back on the idea that the economy was at risk of overheating. He said that prices could show a brief pop in the coming months, as they rebound from very low readings last year, and he said the economy could see a “burst” of spending and temporarily higher inflation when it fully reopened. But he said he expected such increases to be short-lived — not the sustained spiral that many economists worry about.

“That’s really not going to mean very much,” Mr. Powell said, noting that inflation has trended lower for decades. “Inflation dynamics will evolve, but it’s hard to make the case why they would evolve very suddenly, in this current situation.”

A small but influential group of economists is questioning that view — in particular, calling for Mr. Biden to scale back his economic aid plans, which include sending direct payments to most American households, increasing the size and duration of benefits for the long-term unemployed and spending big to accelerate Covid vaccine deployment across the country.

They argue that the size of the package outstrips the size of the hole the coronavirus has left in the economy. With so many dollars chasing a limited supply of goods and services, the argument goes, purchasing power could erode or the Fed might need to abruptly lift interest rates, which could send the economy back into a downturn.

“It’s hard to look at all those factors and not conclude there’s going to be inflationary pressure,” said Michael R. Strain, an economist at the conservative American Enterprise Institute who supported relief efforts earlier in the recession but was among the first economists to warn Mr. Biden’s plans could set off price spikes. “My worry is that by pushing the economy so hard, that will lead to some overheating.”

Mr. Summers, who is an economist at Harvard, warned in a Washington Post column that “judged relative to either the macroeconomic output gap or declines in family incomes, the proposed Covid-19 relief package appears very large.” There is a chance, he added, that Mr. Biden’s efforts “will set off inflationary pressures of a kind we have not seen in a generation.”

Such warnings were a familiar refrain from conservative economists who opposed going big on stimulus during and after the 2009 recession, when Mr. Biden was vice president and Mr. Summers was a top economic aide. They did not materialize: Inflation ran below the Fed’s 2 percent target rate for a decade after the crisis, and Mr. Obama’s $800 billion package has since been judged by many economists to have been too small. That shortfall contributed to sluggish growth and a painfully long recovery for lower- and middle-income Americans.

“The onus should be on anybody who says the economy is about to overheat,” said Austan Goolsbee, a former head of Mr. Obama’s Council of Economic Advisers. “There have been many prominent voices saying that — that there was about to be inflation — for more than 10 years.”

And the fact that the Fed is brushing off overheating concerns is emboldening some Democrats.

“Earlier today, Fed Chair Powell gave an important speech about the state of our economy and what we need to do to get back on track,” Bharat Ramamurti, deputy director of the National Economic Council, said on Twitter Wednesday. “His remarks help back the case President Biden has been making for the American Rescue Plan.”

Many economists have déjà vu when it comes to overheating warnings. Nathan Sheets, a former Treasury official, was global head of international economics at Citigroup in the early 2010s. He recalls hearing worried murmurs about runaway inflation during meetings from London to New York.

“People were really, really sweating,” he said, noting that he, too, fretted that prices might take off. “It just didn’t happen. The world has changed in meaningful ways and the risks of overheating and high inflation are much less pronounced.”

Inflation warnings are a remnant of the late 1960s and 1970s, when American prices were driven relentlessly higher by wage increases, an oil embargo and geopolitical developments.

The result was uncomfortable — restaurants updated their menu prices with stickers; The New York Times reported in 1980 that Manhattan’s “69 Cents Shops” had decided to rebrand to the “88 Cents Shops” — and the cure was downright painful. After years of rapid inflation, Fed Chair Paul A. Volcker began to lift borrowing costs to staggering levels to cool off the economy. He received car keys from auto dealers who couldn’t make sales and planks of wood from home builders facing a dearth of demand. “Dear Mr. Volcker,” one wrote on a block with a knot. “I am beginning to feel as useless as this knothole.”

But for more than a quarter century, price gains have been surprisingly low — not too high.

In developed economies, including those of Japan, the euro area and the United States, monetary policymakers have actually been trying to encourage higher inflation in recent years. Inflation hasn’t sustainably reached the Fed’s 2 percent target since before the 2008 global financial crisis, looking at a Commerce Department index that strips out volatile fuel and food. Price pressures haven’t substantially exceeded 2 percent since the early 1990s.

Economists have struggled to understand the phenomenon, but they largely think inflation is being held down by a cocktail of aging demographics, changing consumer expectations and limited pricing power in a globalized world where consumers can search online to compare prices.

Market-based inflation expectation measures are hovering right around 2 percent, and consumer inflation outlooks have dipped slightly over the past decade, though one gauge ticked up in a recent reading. If buyers don’t expect higher prices, companies may find themselves unable to raise them, so whatever people anticipate can drive reality.

It’s also hard to see where a big and sustained spike in prices would come from, analysts said.

Airfares, apparel prices and hotel prices all took a hit in 2020 during the depths of the pandemic, and they’re likely to jump sharply as the economy reopens and consumers with money in their pockets take vacations and refurbish their wardrobes, said Alan Detmeister, a former inflation expert at the Fed who now works at the bank UBS.

Yet the price of goods that experienced a jump as workers shifted to home offices — from the category that includes laptop computers to the one that tracks cars — could fall back, weighing down overall gains. Categories that matter a lot to the overall index, like rent and health insurance, are both subdued and slow-moving.

In any case, a temporary bounce-back in prices is not the same as an inflationary process in which price gains continue month after month.

Even if prices do temporarily bounce, the Fed has pledged to be patient in the way it thinks about inflation. In years past — including under Ms. Yellen’s watch — it lifted interest rates before price gains had really picked up to head off potential overheating. The central bank’s new framework, adopted last year, calls for policymakers to aim for a period of above-2 percent inflation so that it hits its goal on average over time.

And besides stabilizing prices, Congress also tasks the Fed with trying to achieve maximum employment. Charles Evans, the president of the Federal Reserve Bank of Chicago, said earlier this month that $1.9 trillion in government spending would have the potential to help the Fed hit its inflation and job market goals faster.

“I’m hard-pressed to see the size of this leading to overheating,” he said.