Statute of Limitations filing deadline is midnight?

Actually, you cannot file the lawsuit at all. Florida's medical malpractice act requires you to go through a pre-suit period before you can file a lawsuit. You have an ability to extend your statute of limitations while you do this but your extension request has to be filed prior to your statue of limitation period expiring. Given that your question was posted after 5:00 PM, you have nothing to lose by filing your extension request online now. Whether it will be valid is another question entirely and would require some research.

Unfortunately, given the unique procedural requirements in Florida eloquently summarized by Mr. Boone, you may not be able to file such a claim within the statute limit. Best of luck.

Then file your extension request if you so desire