The move threw the bloc into crisis as it must be ratified by all 27 member states to come into force.
The treaty now goes to Spain's upper house, the Senate, where it is expected to be formally ratified.
The Senate vote had been planned for late September or early October.
But Miguel Angel Moratinos, Spain's foreign minister, said it could be moved up to July, before the legislators take their summer break, so the treaty "can be ratified as soon as possible".
Spain is one of seven EU states that have still to approve the treaty via the parliamentary route.
The Irish vote dominated a summit in Brussels last week and EU leaders have asked Brian Cowen, the Irish prime minister, to report back in October on what he thinks are the best options.
Other than Ireland, the Czech Republic is the member state which could still cause the biggest problem for the ratification process.
The country's upper house has taken the matter to the constitutional court, which is to rule on whether the text conforms to national laws.