In Florida how long does the spouse have to sign the divorce papers once they have them?
One spouse is not required to sign anything. If the other side is not cooperating then just set the matter before the court for hearing.
I am assuming you mean the proposed Agreement to settle the matter. There are no time limits and you may choose not to sign. Consult with counsel who can review the proposal, explain your rights and review whether the proposal is in your best interest.
If however by "papers" you meant you were served with summons by the sheriff or process server then you have 20 days to respond to the Petition by filing an Answer to the Petition with the Clerk of the Court and providing a copy to your spouse or his attorney.