Hungary and Poland have blocked approval of the EU's budget over a clause that ties funding with adherence to the rule of law in the bloc.
The package includes €750bn (£673bn; $888bn) for a Covid recovery fund.
Ambassadors of the 27 member states meeting in Brussels were unable to endorse the budget because the two countries vetoed it.
Hungary and Poland have been criticised for violating democratic standards enshrined in the EU's founding treaty.
The EU is currently investigating both countries for undermining the independence of courts, media and non-governmental organisations. The clause threatens to cost them billions of euros in EU funding.
EU states had already agreed on the €1.1tn budget for 2021-2027, and the coronavirus stimulus package after a marathon four-day summit in July.
The ambassadors had voted through the clause that made access to EU funds conditional on adherence to the rule of law, because it only required a qualified majority, the German EU presidency said.
But the budget and the rescue package needed unanimous support and were then blocked by Poland and Hungary.
Entire process now hangs in the balance
This is a row that's come to a head after simmering for the past four months. It was back in July, when EU leaders first agreed to club together and raise almost €2tn to spend over the next seven years, as they try to recover from the financial crisis caused by Covid.
At the time, the agreement was hailed as a "magic moment" by the EU Council President Charles Michel, who said it was "unprecedented", because access to cash would be conditional on countries following the rule of law.
But Hungary and Poland haven't viewed the arrangement that way, and both countries have long been at loggerheads with the EU over perceived backsliding of core values.
On Monday, they refused to support the plan. Hungarian Prime Minister Viktor Orbán had sent a note in advance of the meeting, to German Chancellor Angela Merkel and French President Emmanuel Macron, making clear his intention, claiming the rule of law clause "jeopardises trust" between member states.
Final approval needs unanimity, and now the entire process hangs in the balance, with other member states making it clear they desperately need access to the money come January.
"We cannot support the plan in its present form to tie rule of law criteria to budget decisions," said Zoltan Kovacs, a spokesman for Hungarian Prime Minister Viktor Orbán.
Polish Prime Minister Mateusz Morawiecki threatened a veto last week.
On Monday, Polish Justice Minister Zbigniew Ziobro said the rule of law issue was "just a pretext".
"It is really an institutional, political enslavement, a radical limitation of sovereignty," he said.
But Austrian Chancellor Sebastian Kurz, addressing a conference shortly after the budget was blocked, said that "upholding the principles of the rule of law is an absolute necessity" because the sums being handed out by the EU to member states were so vast.
Romanian Prime Minister Ludovic Orban said the rule-of-law clause was an important protection to ensure taxpayer's money is "spent in a just and effective manner".
He called on EU states "to work together" adding: "We need to refocus and get this agreement done."
German ambassador Michael Clauss, who chaired the meeting, warned that the EU would face "a serious crisis" if the financial package was not quickly adopted.
"We have already lost a lot of time in view of the second pandemic wave and the severe economic damage," he said.
In a tweet, Johannes Hahn, EU-Commissioner for Budget and Administration, said he was "disappointed" by the veto.
He urged member states to "assume political responsibility and take the necessary steps to finalise the entire package".
"This is not about ideologies but about help for our citizens in the worst crisis since World War Two," he added.
The impasse will be debated by EU European affairs ministers on Tuesday and by EU leaders in a video-conference on Thursday. However, officials say a solution might take longer to find.