German Chancellor Angela Merkel, caught between the prospect of Greece going bankrupt and domestic pressure against helping the country further, will be searching in the coming weeks for a third way out.

The euro crisis is back on leaders’ agendas, with Greece probably headed for bankruptcy in October if it does not receive a $38 billion installment of emergency loans from its bailout package. And if Greece spins off the euro, the fissures in the 17-country currency zone could rapidly widen, with Spain and Italy also vulnerable.

On Thursday, French President Francois Hollande is set to visit Berlin to urge Merkel to soften her stance. On Friday, Greek Prime Minister Antonis Samaras will make the same trip to plead for forbearance.

Officials close to Merkel say the decisions are among the toughest of her career, with the future of the euro zone balanced against German public opinion and her own political concerns ahead of a 2013 parliamentary election.

Although Merkel and some of her allies have indicated in recent days that they would try to find a temporary solution to forestall a Greek bankruptcy, domestic opinion appears dead set against spending more money to bail out the troubled Mediterranean nation. For now, Merkel’s advisers do not believe they can talk Parliament into spending another cent on Greece.

Samaras outlined his hopes Wednesday in an interview with Germany’s top-selling Bild newspaper, which has been stridently anti-Greek during the crisis. He said his government, in power for only two months, needs more time to meet its commitments.

“Let me be very clear: We are not asking for extra money,” Samaras said. “All we want is a bit of ‘air to breathe’ to get the economy running and to increase government revenues. More time does not automatically mean more money.”

The interview was published hours before Samaras was to meet in Athens with Luxembourg Prime Minister Jean-Claude Juncker, who leads euro-zone countries in their response to the crisis. Juncker told the Austrian Tiroler Tageszeitung newspaper this weekend that a Greek exit from the euro zone “will not happen — unless Greece violates all the conditions and keeps to no agreements.”

Decision is weeks away

Merkel said Wednesday that it would be weeks before she weighs in on what to do about Greece, saying that she would wait for the outcome of an inspection of the country’s finances, led by the European Union, the International Monetary Fund and the European Central Bank and expected in late September or early October. Nor can Merkel make meaningful plans before a Sept. 12 court ruling in Germany that could force the country to change the constitution to push further European economic integration. European officials have focused on an Oct. 18 E.U. summit as decision time for Greece.

Greece’s fundamental economic situation is not in significant dispute. The recession this year is worse than was forecast, with many analysts expecting the economy to shrink up to 7 percent in 2012. Unemployment has spiked to 23.1 percent. And the country’s ability to meet the goals by the dates envisioned in the March bailout package, doubtful from the beginning, was even more endangered by months of delays created by a tumultuous spring election season. Samaras has said he wants to spread Greece’s austerity program over an extra two years, until 2016.

In the elections, Greeks chose pro-euro leaders over ones who would have rejected the bailout altogether. Now Samaras is gambling that Merkel will be loath to cut off Greece before he has had a chance to prove his commitment to overhaul his country’s economy.

His bet may pay off. In recent days, some of Merkel’s allies have started to show more flexibility toward Greece after months of holding a hard line. “Small concessions are feasible provided they are strictly made within the framework of the second aid program,” Norbert Barthle, the budget spokesman of Merkel’s Christian Democratic Union, said in Parliament this week. He suggested lowering the interest payments on Greece’s bailout loans.

A make-or-break move

Other German leaders have shown less tolerance toward Greece, including the leader of the Free Democrats, the junior partner in Merkel’s coalition government. The prospect of a Greek exit from the euro zone “has long since lost its horror,” Philipp Roesler said last month.

Some German analysts expect an accommodation to be found.

“No one wants Greece to default now or in the coming weeks,” said Sebastian Dullien, a senior policy fellow at the European Council on Foreign Relations in Berlin. Even in the longer term, Dullien said, Germany may be skidding toward a recession — something Merkel will be eager to avoid before she is up for reelection next year. “They know that voters wouldn’t be very happy about an increase in unemployment,” he said.

But in the end, Merkel’s response may be shaped by the constitutional court ruling on the legality of the austerity pact and bailout fund that European leaders agreed to late last year. If it rules that the plans hand over an unconstitutional amount of sovereignty to the E.U., Merkel may be forced to seek a referendum to change her country’s Basic Law, in effect handing an up-or-down vote on the future of the euro to the German electorate.

That could be a make-or-break move, unleashing Germany’s might in combating the crisis or cutting it off altogether. And some German leaders, including Finance Minister Wolfgang Schaeuble, think it may be coming.

“There’s no problem with transferring more rights to Brussels, but the German people will have to make that decision,” Schaeuble told Spiegel magazine in June.