EU leaders meet on Friday for the first face-to-face summit since the coronavirus crisis, with low expectations of a deal on a €750bn (£670bn) post-Covid stimulus package.
The main issue is how much of the recovery fund will be handed out in grants and how much in loans.
They also need to agree on a seven-year budget worth another €1.07 trillion.
German Chancellor Angela Merkel warned ahead of the summit that "the positions are still far apart".
The Brussels meeting is due to continue on Saturday but EU leaders may need longer to reach a deal. A French official said an agreement this weekend was possible but certainly needed to be wrapped up by the end of the summer.
Arriving for the talks, Estonian Prime Minister Juri Ratas said a very difficult two days were ahead "but I think we need a fast, strong and united response to the pandemic to kick-start the European economy".
Why is the fund so tricky?
Southern states including Italy and Spain want an urgent decision "not weakened by a lesser compromise", in the words of Italian Prime Minister Giuseppe Conte. They need to revive economies battered by a devastating pandemic that claimed 35,000 lives in Italy and a further 28,400 in Spain.
The Frankfurt-based European Central Bank has already forecast an 8.7% slump in the eurozone economy this year because of the pandemic. But economies that only recently pulled out of a financial crisis want grants rather than taking on further debt.
The recovery plan, backed by France and Germany, for €500bn in grants and subsidies and €250bn in loans, is being resisted by several "frugal" Northern European countries, led by the Netherlands.
The EU recovery fund is already controversial as the money would be borrowed on the financial markets, to be paid back some time after 2027. It's made up of a number of different instruments, but the biggest part of it would be geared to supporting green and digital investment and reform. Some 30% of the funding could be tied to climate projects.
The frugal states, which include Austria, Sweden, Denmark and to some degree Finland, want some control over how the money is handed out. The Southern states say that will hold the process back.
There is also pressure to whittle down the size of the €750bn fund, so the solvency instrument devised to revive companies after lockdown could be under threat.
But Italian Economy Minister Roberto Gualtieri told the Corriere website that Rome "will fight hard not to modify" the structure of the recovery fund.
Why the rush?
Leaders have been criss-crossing Europe ahead of the summit in a bid to find a solution. Visiting Sweden, Spain's Pedro Sánchez warned: "If we delay the response, we delay the recovery and the crisis could get worse."
The head of the European Central Bank, Christine Lagarde, has also urged the EU27 to move quickly on an "ambitious package", warning that uncertainty remains high on the speed and scale of the economic rebound.
If the package of grants or loans is agreed, then France would be able to put €39bn of EU funding towards its own €100bn national recovery plan. Prime Minister Jean Castex said this week that €20bn of that would go towards insulating buildings, and converting cities to using bicycles.
A group of 150 scientists and celebrities joined climate activist Greta Thunberg on Thursday in signing an open letter urging EU leaders to end "all investments in fossil fuel exploration and extraction".
As eurozone economic activity picks up and lockdowns are lifted, there are fears of a second surge.
The ECB has confirmed its emergency €1.35tn bond-buying programme is on track to last until June next year, to help governments, banks and businesses.
Are the Dutch out on a limb?
One of the main issues for EU leaders is whether any country can have a veto over money being handed out to a member state for recovery purposes.
Ahead of the summit, a French official said the Netherlands was the only one of the so-called frugal states seeking strict control of conditions for paying out funds.
Is that true? Certainly Dutch Prime Minister Mark Rutte insists on reforms to pensions, welfare and tax services in return for funding and he wants assurances that the money goes to modernising infrastructure and green investment.
But Finland too wants conditions attached to EU funding, both from the recovery pot and from the wider 2021-27 EU budget.
The task facing EU leaders is to agree not only on the size and terms of the recovery fund, but the overall EU budget too.
And Hungary's Viktor Orban has threatened to derail both the fund and the budget if any payments are linked to a member state's rule of law.
His ruling Fidesz party has been suspended by the big European People's Party bloc for clamping down on media and civil society.
"We could veto it because it needs a unanimous decision. Hungary could say no," Mr Orban said last week.