France and Germany are pushing through rules that include include tougher penalties on countries that break the EU rules concerning national debt.
The Lisbon treaty took five years to negotiate, and came into force last December.
The motive behind the proposed amendments is to avoid another Greece-style economic meltdown, with Germany arguing that it also needs the changes to counter domestic political obstacles.
German Chancellor Angela Merkel and French President Nicolas Sarkozy want the treaty renegotiated to set up a permanent rescue fund for members in the red by 2013.
They also want to be able to punish chronic overspenders by stripping them of their voting rights.
European Commission head Jose Manuel Barroso said he could live with "limited" treaty change but that moves to reduce voting rights would be "unacceptable".
Luxembourg Prime Minister Jean-Claude Juncker, who heads the 16-nation group of eurozone finance ministers, agreed.
But Poland, the EU's fastest growing economy that has not yet adopted the euro, is in favour of the amendments.
Prime Minister Donald Tusk said treaty change would "suit us", but described the idea of removing voting rights as "exotic".
Danish Prime Minister Lars Lokke Rasmussen said: "I realise the Germans think they have some kind of constitutional problem and we have to take that seriously."
Greece's George Papandreou said Athens was "opposed to discussion about the removal of voting rights" but saw "no problem in principle in changing the treaty."
Most euro states favour moves to give permanent life by 2013 to a three-year trillion-dollar rescue fund created in the aftermath of the Greek crisis.
But Germany, which contributed the lion's share to the European Financial Stability Fund, said it could not pay into a permanent fund under the current rules of the treaty without risking hostile action from its powerful Constitutional Court.