One of their arguments Thursday in Pensacola is expected to be that Florida and the other 19 states don't have standing to challenge the law.
U.S. District Judge Roger Vinson has said crucial pieces of the lawsuit could go to trial. He wanted to hear more arguments over whether it's constitutional to force citizens to buy health insurance.
A federal judge in Virginia ruled this week against the insurance mandate. Two other federal judges have upheld the health care law, and both sides expect the issue to wind up before the Supreme Court.
Vinson says he won't issue an immediate ruling.