One European official speaking anonymously because of the fluidity of the situation, said that it would probably be possible to go ahead with the bailout without Slovakia, if necessary.

The rules of the E.F.S.F. were laid down in a “framework agreement,” rather than being written into the bloc’s governing treaty. That allows “a certain flexibility,” said the official, adding that “in these sorts of cases, where there’s a will, there’s a way.”

Carving Slovakia out of the financial stability fund would be technically messy and would send a terrible signal about the readiness of all 17 nations to participate in the permanent bailout fund the European Union wants to set up after 2013.

Officials in Brussels say they believe that the vote could be reversed with Mr. Fico’s support as early as the end of the week. But “the political damage of a repeated ‘no’ would be horrendous,” said the official.

That means that negotiations are likely to be political ones, seeking to persuade politicians in Slovakia that it is in their interests to ratify the deal, and pointing out that self-exclusion could be harmful in the future if the Slovaks themselves need aid.

The approval process, which has already lasted over two months, has been excruciatingly complex. At times it has seemed like a strange hybrid of a geography class and a civics lesson, wending its way from Finland in the north to the Mediterranean island of Malta, from Germany’s Federal Constitutional Court in Karlsruhe to a Spanish Parliament surrounded by police barricades to keep protesters at bay.

At each step the union has found a way to muddle through for the sake of unity and fear of the unknown. Those fears center on the repercussions on financial markets and the risk that doubts, and with them speculative attacks, will increasingly spread to large economies like Spain and Italy, should officials fail to contain problems in Greece, Portugal and Ireland.