FRANKFURT, Germany — U.S. Treasury Secretary Timothy Geithner is darting across Europe with a stark message: The continent’s leaders must act quickly and convincingly to defuse a debt crisis that is threatening the global economy.

His visit this week comes on the eve of a summit of European leaders Friday that could yield a plan for resolving the crisis. Optimists hope a deal would persuade investors to lend to countries, such as Italy and Spain, that are straining under crushing debt burdens.

Geithner’s trip to five European cities is the most visible part of a broader drive the United States has been making, publicly and privately, to nudge Europe to resolve its crisis.

The United States has plenty at stake.

A still-fragile U.S. economy remains vulnerable to any financial contagion that might erupt in Europe. If banks that are sitting on piles of European government debt cut off lending, the global economy would suffer. The flow of U.S. exports would slow. A panic could send stocks tumbling worldwide.

And with Obama facing re-election in less than a year, the outcome of Europe’s crisis carries risks for the president personally.

Besides Obama’s trip to press European officials, the U.S. government is acting in other ways:

The Federal Reserve took a leading role last week in crafting a plan with other central banks to make it easier for banks to borrow U.S. dollars and continue lending. The move is a short-term fix that doesn’t lighten Europe’s debt load. But it excited investors, who drew hope that the top economic powers can jointly resolve the crisis.

Obama met privately last month with the leaders of Germany and France to discuss the crisis. Through such personal diplomacy, Obama has been sending an overarching message: Do whatever it takes to fix the crisis.

Vice President Joe Biden, on a trip Sunday to Greece, the first country felled by the debt crisis, warned that time is running short for European leaders.

The United States, the biggest contributor to the International Monetary Fund, is supporting the fund’s bailouts of Greece, Portugal and Ireland.

Analysts say the administration is arguing that Europe must unite behind a single solution that leaves no eurozone nation behind.

German Chancellor Angela Merkel and French President Nicolas Sarkozy have called for changing the European Union treaty to centralize spending and borrowing decisions for the 17 countries that use the euro.

Many analysts say the European Central Bank or the IMF must then respond by providing more financial aid. Germany, in particular, has opposed more aid without a guarantee that all eurozone nations will adopt binding budgetary limits.

“The Americans are doing to the Europeans, and especially the Germans, what the Germans are doing to the Greeks and the Italians – that is, holding their feet to the fire to get them to do something,” said Thomas Kleine-Brockhoff, a senior director at the German Marshall Fund in Washington.

Europe, with its potentially vast impact on the U.S. economy, is a political wild card for Obama. He could face voters with the highest unemployment of a sitting president seeking election since World War II. Unemployment, now at 8.6 percent, was 7.8 percent when Obama took office in January 2009.

“I’m spending an awful lot of time making trans-Atlantic calls,” Obama said at a fundraiser in New York last week.

One senior administration official familiar with Obama’s talks with Merkel and Sarkozy said the president has offered ideas based on his experience dealing with troubled assets, bank recapitalization and government interventions during the U.S. financial crisis. The official added that Obama has stopped short of dictating a solution.

The official, who wasn’t authorized to discuss Obama’s private conversations with leaders, spoke on condition of anonymity.

But advice from the president has its limits, said Bruce Stokes, a senior trans-Atlantic fellow for economics at the German Marshall Fund. For one thing, Germany may be tiring of the U.S. push, Stokes said.

“There’s a bit of frustration with us, in the sense that they keep bringing up: ‘How is it that you’re telling us what to do when you have such debt problems of your own?’”

Referring to the 2008 U.S. financial crisis, Stokes said, “We have an experience where we acted massively, and we wish they would do that. In the history of these crises, you need to act massively and quickly, and the Europeans have done neither.”