Florida is normally a no-fault state however as of October 1, 2007 the no-fault law sunset. The bill to restore Personal Injury Protection, also referred to as no-fault or PIP, was signed into law October 11, 2007. The bill to reinstate PIP took effect January 1, 2008. So FL was basically a tort state from October 1, 2007 to December 31, 2007.
The office of the FL Chief Financial Officer recommends that to make sure that you have coverage in case you sustain any injuries, you should consider purchasing optional medical payments coverage from your auto insurance company. Since PIP was re-enacted you should still be able to purchase Non-Statutory PIP between October 1, 2007 and January 1, 2008.
You would also want to make sure you have Bodily Injury Liability during this time period. If you have already been responsible and purchased it, you may want to increase your bodily injury liability coverage (in case you injure another person and are at fault) and uninsured motorist coverage. Uninsured/Underinsured Motorist Bodily Injury is also now more important in Florida.
If you did not have Bodily Injury Liability coverage and were found at fault in an accident where the other party involved was injured and they did not have their own PIP or other medical coverages to make a claim for their bodily injuries then they would likely seek resolution for their medical expenses through litigation and the courts.
So, yes during the period of time that PIP is not required of drivers in Florida if you cause bodily injuries to others and there are not insurance coverages available for that driver to make a claim through then that party could take legal action and sue you. If both drivers in the accident have PIP coverage than legal precedence is set to allow for the claim to be filed as a no-fault claim, which removes some of the ability for lawsuit.