Government spokeswoman Maria Jesus Montero said Europeans will begin to lose trust in the EU if it does not act together in the crisis, which she compared to the Second World War.
"We need the help of other countries, and that's why the European Community was originally formed, at that time after a physical war, now we are fighting a war against an epidemic," she said in an interview on Antena 3 TV channel.
Agriculture Minister Luis Planas echoed that concern.
"This is a crucial issue on which the European Union's future is at stake," he told Sur Radio station.
However, both also said they were optimistic further negotiations would eventually yield positive results, even though EU finance ministers failed to reach agreement in all-night talks and suspended their meeting until Thursday.
"My take is that even though it may take a lot of time and a lot of meetings, we'll reach a positive agreement," Planas said.
Sources and officials said a feud between Italy and the Netherlands over what conditions should be attached to euro zone credit for governments fighting the pandemic was blocking progress on half a trillion euros worth of aid.
Issuing joint debt has been a battle line between economically-ailing southern countries like Spain and Italy and the fiscally-frugal north, led by Germany and the Netherlands, since the financial and euro zone crises began over a decade ago.
To support economies burdened by coronavirus lockdowns, the EU has already suspended state aid limits and allowed member states to inflate their debt to spend more.But Spain, France, Italy and other countries say that is not enough and have cast the discussion as an existential test of solidarity within the bloc.