The leaders of Germany and France are pushing their European counterparts to save the ambitious project of continental unity that grew from the ashes of World War II.
At stake at the summit in Brussels, which began Thursday evening, is the future of the euro, the stability of the global financial system and the balance of power in Europe.
To convince financial markets that Europe's economy-crushing debt crisis is a one-time event, countries will have to give up significant powers, such as some decisions on borrowing and spending, to a central authority.
President Nicolas Sarkozy and Chancellor Angela Merkel face daunting challenges: the need for unanimity among 27 national leaders, if they choose to work within the EU; the burden of convincing the 17 countries that use the euro to yield some control over their national budgets; the need to do something that will inspire confidence in the financial markets.
For the summit to be declared a success, at a minimum the 27 leaders gathered in Brussels "should agree on some kind of fiscal plan in terms of governance," said Paul de Grauwe, an economics professor and EU expert at the Catholic University of Leuven, in Belgium.
And that plan must be good enough to convince the European Central Bank to intervene in the government bond markets in a manner large enough to stop the panic there, de Grauwe said.
The European Central Bank said it currently has no plan to increase the scale of its bond interventions, which keep down the borrowing costs of weak countries like Italy and Spain, as markets had been hoping. Stocks and the euro fell, while the borrowing rates for Italy and Spain skyrocketed.
ECB chief Mario Draghi had hinted last week that if governments agree to tighter budget controls, the central bank might step up support. Analysts said his comments on Thursday served to keep pressure on politicians to reach a deal.
Merkel and Sarkozy will bring to the EU summit a proposal to force European countries to balance their budgets and to automatically sanction rule-breakers. They want to enshrine the tougher budget oversight in a treaty, either by changing the existing EU treaty or creating a new one for the 17 eurozone nations that others could opt in to.
"Words alone are not believed anymore because too often we did not live up to our words," Merkel told a rally of fellow European conservatives in Marseille, France, ahead of the summit.
But huge divisions remain.
Some countries resist the idea of giving up some of their control over national budgets. Furthermore, the 10 EU countries that don't use the euro are worried about being left out of important decision-making if eurozone countries adopt a new treaty of their own.
European Council President Herman Van Rompuy and some smaller countries that have stuck to the budget rules in the past, meanwhile, are pushing for much more intrusive powers for European institutions to essentially take over wayward states' fiscal policies that even France and Germany are unlikely to accept.
David Cameron, Britain's prime minister, has said he will defend his country's interests at the summit and demand safeguards in asked to amend the EU treaty. He's worried that new eurozone rules could endanger London's role as a global financial center and weaken British economic links with the rest of the region.
However, arriving in Brussels, Cameron appeared to soften his stance somewhat, saying that he would support treaty change if it helped the eurozone emerge from the crisis.
The EU treaties have often been difficult to agree and amend over the past decades.
The latest version, the treaty of Lisbon, was rejected in an Irish referendum before being approved in a second vote.
Before that, the Treaty of Maastricht paved the way for the common currency in 1991. Francois Mitterrand and Helmut Kohl, the French and German leaders at the time, are regarded now as historic figures in European integration.
The question two decades later is whether Sarkozy and Merkel, as leaders of the two most powerful countries in the eurozone, can rise above domestic political fears and reach for their moment in history. Or will they allow the dreams of their predecessors to fall apart.
Dutch Prime Minister Mark Rutte said it is vitally important to include all countries in any new agreement.
"We also have to make sure that we keep the union of the 27 together," Rutte said as he arrived at the summit. "It is not only a union of the 17 eurozone nations. It is also of the utmost importance for us that we also keep countries like Britain, Sweden and the Baltics and Poland united."
Markets have mostly risen since last week on hopes that an agreement among European governments on the Franco-German plan would pave the way for the ECB to intervene more aggressively to support eurozone bond markets.
However, investor optimism was deflated on Wednesday, when a German government official said it could take up to Christmas to clinch a deal, and then again on Thursday, when ECB chief Draghi lowered expectations that the central bank might step in with more help.
An ECB rate cut, and more support for banks to get money flowing through the banking system were not enough to keep investors happy.
Markets were hit again a few hours later, when a European regulator said banks have to raise about 115 billion euros ($154 billion) to meet a new standard meant to inoculate them lenders against market turmoil, including bad government debt.
That's about 8 billion euros ($10.73 billion) more than what the European Banking Authority previously estimated, and bank stocks around the continent plummeted.
An alternative to support from the ECB could be greater help from the International Monetary Fund. Some European leaders have said that their national central banks could lend money to the IMF, which could act as a backstop for financially weak eurozone countries.
A European Union diplomat, speaking on condition of anonymity because talks were ongoing, said eurozone leaders are likely to agree to give the IMF 150 billion euros ($200 billion) in bilateral loans to use as a firewall in the debt crisis.
But officials from other countries dampened expectations that that deal could be finalized by Friday.
The money would come from the central banks of the 17 euro nations, not governments, which are already highly indebted.
The diplomat added that eurozone leaders hoped non-eurozone countries would contribute an extra 50 billion euros ($67 billion).
With so much at stake on the summit's results, U.S. Treasury Secretary Timothy Geithner was zipping across Europe on a three-day trip to press the region's leaders to solve their differences.
Reforms to deal with the debt crisis are "vital" but their implementation will take some time, Geithner said in Milan, where he met Italy's new Premier Mario Monti.
Secretary of State Hilary Clinton, who was in Brussels, said the United States was willing to offer assistance. "But we do need a plan to rally behind, to know the way forward."
© Copyright 2016 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.