With Europe falling deeper into crisis and Congress paralyzed, only one institution may have the flexibility to try to keep the U.S. economic recovery on track: the Federal Reserve.

But the Fed faces a daunting burden. Any new action could provoke tough political criticism. Republicans, in particular, have expressed deep concern about the measures taken by the Fed to support the economy — and could be doubly upset if new efforts goose the stock market and are perceived to work in favor of President Obama’s reelection.

“The Fed is going to try to do the right thing,” said Vincent Reinhart, a longtime Fed economist and now top U.S. economist at Morgan Stanley. But, he added, “The headline they most worry about is ‘The Fed acts to help the incumbent.’ ”

The central bank fiercely guards its independence from politics. But its unprecedented efforts over the past four years — rescuing banks and printing trillions of dollars in new money to support the economy — have raised concerns among conservatives about a rising risk of runaway inflation and a weakened dollar.

In recent months, amid improving economic data, the Fed sent signals that it was pausing its campaign of economic stimulus. But with the escalating crisis in Europe and the sudden slowdown in U.S. economic growth — marked by last week’s report of paltry job growth — many economists say the Fed is likely to reconsider measures to support growth.

Fed Chairman Ben S. Bernanke could provide a hint of whether new stimulus is likely when he testifies before Congress on Thursday.

The central bank could take a relatively modest step, such as a firm commitment to keep interest rates low for several years, or a much more dramatic one — for instance, printing hundreds of billions of dollars to purchase Treasury bonds and mortgage assets.

These steps could bring down interest rates, which already are at historic lows, to further support lending and economic activity. Yet the Fed’s actions are not likely to be a panacea for the economy’s ills — just as they haven’t been in recent years — and couldn’t fully insulate the economy from Europe’s problems.

“We’re getting so close to the election. Rates are already at record lows. What are we trying to accomplish by lowering rates even further?” said Joseph LaVorgna, chief U.S. economist at Deutsche Bank. “Republicans are going to say the Fed’s trying to spike the punch bowl and help the Democrats out because we’re getting closer to the election.”

Diane Swonk, chief economist at Mesirow Financial, argued that should the Fed act in the face of criticism, it will demonstrate its independence. “People accuse the Fed of being political in so many ways, and the fact that the Fed does what it wants is what makes them independent,” she said.

There is a long history of the Fed feeling political pressure — particularly from presidential candidates. Richard M. Nixon blamed his 1960 loss in part on the refusal of Fed Chairman William Martin Jr. to lower interest rates. When he became president, Nixon installed a Fed chair, Arthur Burns, who he believed would be vulnerable to pressure.

After losing the 1992 election amid a weak economy, President George H.W. Bush complained that Fed Chairman Alan Greenspan had refused to lower rates. “I reappointed him, and he disappointed me,” Bush famously remarked.

Bernanke, appointed by President George W. Bush and reappointed by Obama, has faced more pressure from the political right than from the incumbent president. All of the candidates in the GOP primary this year said they would replace Bernanke as Fed chair.

With plans to step down in 18 months, Bernanke may not care much about any criticism leveled at him — but he does care about the Fed’s ability to preserve its independence over the long term.

Last week, Republican presidential candidate Mitt Romney said he thinks additional efforts by the Fed to support economic growth would be unwise.

“I don’t think we are looking for more,” Romney said on CNBC. “I think the right course is to have steadiness from the Fed, to maintain an effort to have a strong currency and a predictable currency.”

Many economists say the Fed did an able job of managing the financial crisis, but its performance in the years since has been a subject of debate. While Republicans have offered a broad critique, so, too, have several prominent economists on the left, such as Paul Krugman, who say the Fed has failed to address persistently high unemployment.

Some Fed veterans say the Fed is used to operating in a hothouse and won’t be swayed by politics.

“I would guess that they’d prefer [to] stay out of the political debate if they could,” said Don Kohn, a former Fed vice chairman. “But they’re already there, and at least in my experience the policy debate has always started and ended with what’s the right thing to do to meet our legislative objectives.”

But Reinhart, the former top Fed economist, said central bank officials must be worried about whether lawmakers in the next Congress will try again to more closely scrutinize their activities. One GOP lawmaker this year introduced a bill to strip the Fed of its charge to keep as many people employed as possible — in addition to ensuring stable prices.

Outside economists say the Fed will certainly act if the economy worsens signficantly. But if it is in a gray area, political considerations could make a difference.

“If it’s close to a 50-50 call for the Fed on whether to act, I could see the political factor as something that could tip the balance to no action,” said Nigel Gault, chief U.S. economist at IHS Global Insight. “But if it’s a clear-cut case, as it would be if the euro-zone crisis worsened sharply, triggered perhaps by a Greek exit from the euro, then the Fed will act, regardless.”