- The head of the European Parliament says all EU members might be asked to chip in
- Leaders have to figure out how to boost the rescue fund trying to handle the crisis
- Some analysts say the fund, the EFSF, needs 2 trillion euros
- EC President Herman Van Rompuy praises leaders' political courage
Europe's top leaders are meeting Sunday in Brussels to hammer out a solution to the debt crisis threatening the common currency, the euro, and -- potentially -- banks around the world.
The European Council meeting comes on the heels of an agreement to funnel more money into European banks to protect them from almost certain defaults by Greece and possibly other European countries.
The deal, agreed in principle by finance ministers Saturday, could be worth around 100 billion euros ($138 billion).
The exact amount must be determined by European leaders, who must also figure out how much of a loss they will ask private investors to accept on Greek debt -- euphemistically known as a "haircut."
And they have to work out how they will boost the rescue fund trying to deal with the crisis, the European Financial Stability Facility, which some analysts say could need a war chest of 2 trillion euros ($2.7 trillion.)
European Parliament president Jerzy Buzek told CNN a deal would be reached by Wednesday at the latest, when EU leaders hold their next crisis meeting.
"We need a comprehensive package and we need to be united ... A strong signal from the EU that we are united is important for the markets," he said.
Buzek said it was possible that other countries from outside the eurozone would be asked to contribute to the bailout fund -- which may be controversial among the 10 EU nations that do not use the euro, including Britain.
"I am sure the solution for the eurozone will be spread among all 27 EU nations because we need the democratic scrutiny," Buzek said.
Italy's Prime Minister Silvio Berlusconi met with key players in the EU Sunday morning, his office said, amid fears that his country could be the next victim of the debt crisis.
He sat down with French President Nicolas Sarkozy and German Chancellor Angela Merkel, as well as European Council President Herman Van Rompuy and European Commission President Jose Manuel Barroso.
Van Rompuy struck an optimistic tone in his opening remarks as the European Council meeting opened Sunday.
"Today we will agree on measures to stimulate growth and to create jobs. We will also deal with the crisis in the Eurozone," he said.
"Our meetings of today and Wednesday are important steps - perhaps the most important ones - in the series to overcome the financial crisis, even if further steps will be needed," he said.
Van Rompuy conceded that some measures "were and are unpopular," and he thanked EU leaders "for your political courage, often underestimated. But these steps forward also require simple and plain hard work."
The European Council consists of the heads of government of the 27 members of the European Union, plus Van Rompuy. They are meeting Sunday morning, after which the 17 nations that share the euro will have an additional summit.