With much of Europe in recession and the United States at risk of falling back into one, the world’s most powerful central banks face enormous expectations this week as they meet to consider new steps to bolster economic growth.

The Federal Reserve is likely to say it plans to keep interest rates low through 2015, signaling that the central bank’s leaders expect U.S. unemployment to remain high for that period, economists say. The Fed’s policymaking committee, which finishes its two-day meeting on Wednesday, is under pressure to act because elected leaders have failed to take steps that many economists consider vital to strengthen the U.S. economy.

On Thursday, the European Central Bank is scheduled to meet and decide whether to act on ECB President Mario Draghi’s pledge last week that it will “do whatever it takes to preserve the euro.”

That dramatic statement raised hopes among many world leaders and global investors that the ECB would escalate its efforts, in combination with strong European governments like Germany, to buy up huge amounts of Spanish and Italian government bonds. The aim would be to ease the debt crisis facing those countries and the financial troubles buffeting the continent. Stock markets surged last week on the newfound optimism.

But the actions by the Fed and ECB aren’t likely to dramatically change the prospects for the U.S. and European economies. Markets fell modestly this week after hopes about central bank action faded into a more sober realization about the limits of what they can do.

In the United States, the Fed has been waging a campaign for four years to stimulate economic growth, but the efforts have been growing less effective.

The main domestic threat to the economy is a series of deep federal cuts in spending and sharp tax hikes set to take effect at the end of the year, which are expected to plunge the economy into recession.

Only Congress and the president can avert that outcome.

In Europe, the ECB has reluctantly become the first responder to the continent’s financial crisis.

After Draghi’s comments last week, anything short of a dramatic bond purchase program may disappoint investors who have seen the continent’s political and economic leaders routinely underestimate the depth of the financial challenge.

Over the long run, however, the ECB can only provide temporary support to the European financial system. To achieve economic growth and stability, leaders in Greece, Spain, Italy and elsewhere must make tough political choices about how to manage their government finances.

Greek leaders will need to reassure the country’s creditors that government debts can be reduced without undermining economic activity. Spanish leaders will need to make sure that their country’s banking system can weather its difficulties, while both Spain and Italy must take steps to stimulate economic growth without being profligate.

While the ECB can prevent an “immediate financial implosion, it cannot itself engineer the adjustments required to set the stage for a revival of investment and employment,” said Michael Gavin, an analyst at Barclays Capital, in a research note on Tuesday. “That will take forceful policy action and time.”

In the United States, the Fed is meeting amid a worsening economic climate. Several months of employment data have been disappointing, and economists say the economy is slowing. The unemployment rate has been stuck above 8 percent.

New steps under consideration by the Fed to bolster growth are likely only to have a modest effect. Interest rates — the main mechanism through which the Fed operates — are already near record lows.

The Fed “is getting very close to its limits,” said Jonathan Wright, an economics professor at Johns Hopkins University.

On Wednesday, the Fed may extend the time it plans to keep interest rates low for an added year beyond late 2014, its current plan. According to economic study conducted by Fed economists, adopting the longer timeline would likely have just a small effect on unemployment. The jobless rate at the end of this year would be 8.29 percent, compared to 8.35 percent under the current plan, the study showed. The effect next year could be larger.

The Fed is also contemplating a new round of asset purchases. By acquiring Treasury bonds and mortgage bonds, the Fed would inject more money into the economy, making interest rates lower. The Fed has already undertaken two rounds of asset purchases, known as quantitative easing.

The central bank followed those measures with other steps intended to lower the interest rates that consumers and businesses pay. In “Operation Twist,” the Fed sold short-term assets and bought long-term ones. The program was renewed in June through the end of the year.

A wide range of economic research has examined the impact of these programs. The effects can be hard to discern, because stock prices and bond market rates are affected by a variety of factors.

In particular, U.S. interest rates have come down largely because global investors, frightened by economic upheaval in Europe, have been piling into U.S. Treasury bonds and other securities for safety.

Still, the research has showed “some diminishing returns” to the Fed’s efforts, said Michael Feroli, chief U.S. economist at JPMorgan Chase.

Economists say the first round of asset purchases, in early 2009 during the worst of the financial crisis, probably had the biggest effect, providing increased confidence and reducing borrowing costs by perhaps half a percentage point.

Later efforts may only have had a quarter or a fourth as much impact, according to research.