Recession has taken hold in parts of Europe, and the euro zone’s stubborn crisis risks a worldwide shock. Growth is slowing in major developing nations, and the U.S. economy may be faltering.

When world leaders take stock at a summit next week in Mexico, they’ll face the discomforting fact that four years of crisis-fighting, trillions of dollars in government stimulus spending and a massive effort from the world’s central banks have failed to produce the “strong, sustainable and balanced” world economy they are striving to build.

Is it time to open the cash spigot again?

“That would be highly due,” said George Pagoulatos, an economics professor who has watched this battered Mediterranean country cut wages in hopes of making its exports more competitive — only to find its major trading partners facing problems of their own. “There is no global demand and no demand in the euro zone,” a situation that leaves Greece with a worsening recession and no clear path to renewed growth.

Investors may be banking on policy action. On Tuesday, U.S. markets gained on speculation of a coming stimulus measure from the Federal Reserve after next week’s Fed policy meeting and after the European Central Bank endorsed a plan to guarantee bank deposits, Bloomberg reported.

Charles Evans, president of the Federal Reserve Bank of Chicago, told Bloomberg TV that he would support a variety of measures to accelerate hiring, especially more stimulus. “I’ve been in favor of pretty much any accommodative policy I’ve heard about,” Evans said in the interview. The non-voting Fed official echoed remarks made last week by three voting members of the Fed board, who expressed support for more central bank action if the U.S. economy continues to weaken.

The slowdown in growth is acute in Greece, where a multi-year downturn, a financial and debt crisis and now a political stalemate have combined to potentially force Greece to drop the euro and unravel a currency union intended to be “irrevocable.”

But there is heightened concern that the global economy as a whole is running out of steam — that the massive amounts of fiscal stimulus and loose monetary policy used to battle the 2008 recession have failed to nurse the world through an era of shaky growth, stagnant wages and high unemployment.

The World Bank cut its forecast for world economic growth to 3 percent for 2013 on Tuesday, maintaining its 2.5 percent growth forecast for this year. The bank cited the European debt crisis as a threat to developing markets, saying that “should the situation in Europe deteriorate sharply no developing region would be spared.”

Major political efforts to quell Europe’s problems have come up short: Even after regional officials committed $125 billion to bolster Spain’s banks over the weekend, the country’s borrowing costs rose again on Tuesday — to their highest level since the country adopted the euro — amid speculation that the amount may not be enough or that the government may also need help. Interest rates on government bonds also jumped in Italy as that country’s prospects for economic growth dim alongside the euro zone’s.

Weak job creation in the United States has triggered concern about the health of the world’s largest economy, which only a few weeks ago the International Monetary Fund had judged to be “gaining traction.” Growth has ebbed in major developing countries, including China, India and Brazil.

Leaders of those and other major nations will gather in Mexico next week for the annual meeting of the Group of 20, an organization intended to serve as a steering committee for the world economy. The group proved its mettle in the wake of the Lehman Bros. collapse, when summits in Pittsburgh and London produced a global round of stimulus credited with staving off an outright depression.

Since that example of crisis-driven coordination, however, nations have pushed their own agendas and, with the economy appearing to heal, deferred more to local politics. Germany championed a global round of deficit-cutting that now seems ill-timed; the United States sniped at China over its currency and other policies; and Brazil sniped at the United States for printing too much money. The issue in Mexico is whether the risks of a new recession have gotten bad enough that global action is possible.

“There is a strong case to be made” for a broad effort by central banks and governments to boost incomes in the short term and try to preempt another downturn, said Edwin Truman, an analyst at the Peterson Institute for International Economics and a former Treasury Department adviser. “We may not be at the point where we declare a global recession, but you are close.”

Individual nations have already taken some action or put ideas on the table. The Obama administration has argued that nations need to pay more attention to growth, both to ease unemployment and as the only sure way to tackle high public and private debt. President Obama has proposed a $500 billion jobs bill. The argument has gained traction with the spread of problems in Europe and the election of socialist President Francois Hollande in France. China and Brazil have both eased monetary policy. European nations are debating how to balance strategies to boost income and jobs with soaring debt.

But that is far short of what was done in 2008 and 2009, when the Federal Reserve began propping up world markets with unlimited dollar loans and supporting U.S. markets with targeted asset purchases, China embarked on a major public infrastructure program that boosted its imports of U.S. and European equipment, and European nations borrowed freely to rescue their banks and fight off recession.

Whether similar measures can congeal over the next week in part depends on the hangover from that round of stimulus. Nations such as Italy, France and Britain, for example, may be near the limit of what they can comfortably borrow; Obama’s jobs bill is stalled in Congress, and other proposals may face the same fate.

Some analysts, moreover, argue that it is time to focus more on long-run policies and accept the fact that growth in the developed world will be slow until debt is cleared away and nations become more competitive.

“If this were just a problem of confidence, you could step in and create demand in the short term,” said Hans Timmer, a top World Bank economist and author of a recent bank review of global economic conditions. “This is a situation where many economies created lots of problems in the boom period that have to be solved. . . . Just by stimulating the economy you are not solving the problem.”

The slowdown in China, he argued, is to be expected after the boom years early in the 2000s and the fast recovery from the 2008 crisis. Officials in Beijing should not be encouraged to do any more than they’ve already done to ease bank lending, he said.

“There is no reason for China to suddenly go out with more stimulus,” he said.

The final outcome in Mexico could turn on a variety of issues. Greece, for example, on Sunday will hold elections that could prove either reassuring — if a centrist coalition returns to power — or destabilizing, if a leftist coalition wins and scraps an international bailout.

The G-20 meets the day after the vote. The U.S. Federal Reserve board meets that week, as well, and some analysts argue that if stimulus is going to come, it will be up to the central banks — not indebted governments — to deliver it.