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The EU treaties often have been difficult to agree to 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, respectively, at the time, are regarded now as historic figures in European integration.

The question two decades later is whether Mr. Sarkozy and Mrs. 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,” Mr.  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 mostly have 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 Mr. 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 already are highly indebted.

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