The House vote came on the day that many experts saw as the deadline under federal law for naming electors.
The special session was called by Republican legislative leaders, who maintained that they were being forced to name electors.
Democrats accused the Republicans of tactics intended to drag out the lawsuit past Dec. 12, when the Legislature will have named presidential electors.
If the Legislature is allowed to name electors on its own authority, it will establish a devastating precedent.
Increasingly, senior Republican legislators are talking about naming electors by resolution, which does not require the governor's signature.
Republicans in both Houses initially said that the legislation was required to ensure that Florida met the Dec. 12 deadline for naming electors, while Mr. Gore contested the election.
Federal law requires states to name electors by Dec. 12, six days before the Electoral College meets.
The Legislature may decide to name electors of its own choice if the court fights remain unresolved by Dec. 12.
And facing a Dec. 12 deadline for the state to name electors for the Electoral College, Mr. Gore has no days to spare.
The Republican-dominated Legislature is in special session to name electors itself, almost certainly pledged to Mr. Bush.