President Obama’s effort to contain the European debt crisis is taking on greater economic and political urgency as Europe emerges as the greatest threat to the faltering U.S. recovery and, potentially, a significant hurdle to his reelection prospects.

At the Group of 20 summit in Los Cabos, Mexico, this week, the president is expected to press European leaders to do more to stabilize their banks, stimulate job growth and prevent debt-stricken Greece from dropping out of the euro zone.

Failure to find a solution in Europe could plunge the world deeper into recession, according to Obama administration officials and many independent economists.

“Obviously, the situation in Europe will be central in leaders’ minds when they arrive in Los Cabos,” said Mike Froman, deputy national security adviser for international economics, at a White House briefing Friday. “It’s the dominant risk to the global economy at the moment. And Europe is our largest trading partner and a key part of the global financial system, and therefore it’s very important to the United States.”

A May jobs report showing more anemic growth than most economists had anticipated indicates the U.S. economy is newly vulnerable to what Obama last week called “head winds” being produced by the European crisis. With most Americans deeply uncertain about their financial circumstances and the president’s economic stewardship, a turn for the worse in Europe could bring political head winds for him, too.

“The stakes are so high,” Froman said about the economic dangers. He could have easily been talking about the president’s political fortunes.

The European crisis is worsening at a moment when the domestic economy has emerged even more clearly as the defining issue of the 2012 presidential campaign. Obama held a rare news briefing at the White House last week to underscore the urgency of the situation across the Atlantic, where drastic reforms, pushed primarily by German Chancellor Angela Merkel and meant to reduce high government debt, threaten to choke growth and worsen the crisis in the short term.

This week, Obama and his Republican opponent, Mitt Romney, delivered dueling speeches on opposite sides of Ohio intended to frame the election as a stark choice of how to lead the United States back to prosperity. While Romney argued that Obama’s spending and regulations have gotten in the way of job creation, the president said Romney’s plan for tax cuts for the wealthiest Americans and austerity would cripple growth and decimate government programs that strengthen the middle class, such as education, job training and infrastructure improvement.

Obama’s ability to speak frankly about the European crisis is complicated by his dual roles of chief executive and candidate. It would suit Obama’s political message to convey sharply to European leaders what he believes they should do to shore up their economies. He comes down squarely on the side of growth and stimulus — on the opposite side of Merkel’s austerity campaign.

But it would be awkward for him to engage in a public debate with allies over how to solve their problems. And diplomatically, if the American president is seen lecturing Europeans on what course to take, it could produce the opposite effect.

“There’s a limit of how far the president can lean forward on this,” said Matthew P. Goodman, who worked for Obama as director for international economics on the National Security Council and is now with the Center for Strategic and International Studies. “The view in the administration is that criticism of Europe at some point becomes counterproductive. The foreign countries listening to this end up feeling the U.S. is badgering them or pushing them too far.”

As a result, it is Obama’s surrogates (most notably former president Bill Clinton) and not the president himself warning that Romney’s proposals to slash spending and cut taxes could extinguish the recovery much like Europe’s austerity measures are doing there.

Romney, meanwhile, is operating under no such constraints. In nearly every speech, the former Massachusetts governor accuses Obama of following Europe down the path of high debt and fiscal insolvency. “Did you see the numbers in Spain? Twenty-five percent unemployed,” Romney declared at a rally in Weatherly, Pa., Saturday. “You know what’s happening in Greece, with low wage growth? That’s where the policies of Europe lead. I don’t believe Europe works in Europe. I don’t want it here.”

Although talk of the European economy is widely expected to dominate the G-20 summit, Obama is also scheduled to hold one-on-one talks with Mexican President Felipe Calderon, Chinese President Hu Jintao and Russian President Vladi­mir Putin.

The meeting with Putin will be closely watched in part because it comes just days after Secretary of State Hillary Rodham Clinton accused Russia of causing a “dramatic escalation” of the crisis in Syria by shipping helicopters to the regime there.

Although pro-Europe parties won a slim victory in Sunday’s elections in Greece, the uncertainty over Europe has prompted discussion of contingency plans in the event a global economic crisis arises.

Lael Brainard, the undersecretary of the Treasury for international affairs, declined to say whether the United States had prepared such a contingency plan when asked about it at the White House briefing Friday.

“The president recognized very early on that we needed to help insulate our economy, we needed to provide an insurance policy, that our recovery was still quite vulnerable to head winds from Europe,” Brainard said.

Few expect concrete actions or plans to emerge from the summit; rather, the expectation is that European leaders will begin discussing what they hope to achieve at their own summit at the end of the month.

The Obama administration hopes to continue pushing European leaders toward more government spending as a way to revive their economies, an effort that began at a Group of Eight summit last month at Camp David. The White House announced, with some fanfare after that summit, that European leaders had tentatively agreed that a growth agenda, rather than strict fiscal austerity, was the right path to prosperity. Since then, however, Merkel has signaled that Germany alone cannot bail out Europe, raising doubts about her intentions.

The United States can offer European leaders cover as it pushes them to take steps similar to what this country’s leaders did in 2008 and 2009 to avert a far deeper downturn.

“People know we’re the largest economy in the world, the market most important to the world,” said Goodman, the economist. “Our experience is valuable. What we can do is provide a little air cover to the Europeans as they try to deal with difficult domestic political choices.”

He added: “The European Union is, as a whole, the largest economy in the world, so there is a huge risk if Europe goes into crisis or has negative growth, and there look like strong prospects for that. At minimum, the president has an interest in getting the Europeans to address that.”

Staff writers David Nakamura and Philip Rucker contributed to this report.