France and Germany, traditionally leaders in such integrationist moves, are at loggerheads over parts of the plan, and there is little time left for the EU to meet a commitment to complete the framework for banking union by the end of the year.
Critical questions remain unanswered, such as how many banks the ECB should directly supervise and whether the central bank gets longer than one year, as planned, to fully take on its role.
After three years of piecemeal crisis-fighting measures, agreeing on a banking union would lay a cornerstone of wider economic union and mark the first concerted attempt to integrate the bloc's response to problem lenders.
But reaching a deal, which EU leaders want to sign off when they meet at a summit on Thursday and Friday, will require addressing the concerns of Germany, whose support is crucial, while also satisfying France and others with deep vested interests such as Britain, Sweden and the Netherlands.
"It's not an easy one for Germany," said one diplomat, close to the talks. "But the markets are watching us."
Another diplomat said it came down to a conflict between quality and speed: For the best banking union possible to be put in place it will take time and it may be necessary to extend agreed deadlines.
Berlin is concerned that supervision will develop into a scheme under which it is left to foot the bill for European banks too weak to survive when, as is planned, a central resolution scheme is set up to close troubled lenders.
It is also worried about a potential conflict of interest between the ECB's double role as supervisor and as guardian of monetary policy. Such a conflict could arise if the ECB were to decide to keep interest rates low to prop up banks.
In a sign of the tensions last week, German Finance Minister Wolfgang Schäuble publicly clashed with France's finance minister at a meeting intended to finalise the plan.
Schäuble objected to the ECB's Governing Council having the final say over monitoring banks, a stance that appeared to push the talks backwards. One official from a non-eurozone country said on Tuesday that Schäuble had softened his line since.
But France also has demands.
"We can envisage degrees of supervision depending on banks' size, but on one condition - that in the end the European Central Bank holds the ultimate responsibility," Finance Minister Pierre Moscovici told Reuters earlier this week.
This concern is shared by analysts. "The ECB ultimately is the Governing Council," said Guntram Wolff of Bruegel, a think tank in Brussels. "Not leaving the final say with the Governing Council means you create a new institution. If you create a new institution, it would not have the credibility of the ECB."
Cyprus seeks compromise
Cyprus, which as holder of the rotating EU presidency chairs the meeting, will put a proposal for compromise before the ministers.
In the compromise document obtained by Reuters, Cyprus recommends that banks with assets of €30 billion or with assets larger than one fifth of their country's economic output be supervised directly by the ECB rather than national supervisors. Critically, however, they leave the ECB with the authority to widen this remit to problem banks.
The central bank's Governing Council would keep the final say in supervision, according to the proposal, which also lays emphasis on the need for a clear separation between monetary policy and supervision.
Ministers will also examine a Cypriot suggestion to allow the ECB take longer than until 1 January 2014 to fully take on its role.
EU leaders hope that by setting up a single banking authority and later establishing a resolution fund for distressed banks, they will stop troubled banks from dragging their countries into crisis. They also hope to set up a way of coordinating national deposit guarantee schemes.
But while most countries support the idea of supervision, which is the first pillar of a full banking union, they disagree on how to structure it and how far to go in sharing bank risks.
All 27 countries in the European Union must give their approval for the project to go ahead, even if only those countries in the eurozone will fall under the banking union to begin with.