Federal courts will continue to operate normally until October 17th when they run out of money; coincidentally the same day our government will default if it doesn't raise the debt limit.  After October 17th, it is likely that criminal cases will continue unabated due to constitutional speedy trial requirements.  Civil matters, on the other hand, will likely be sidetracked by the Courts.  In the Middle District of Florida (covering Jacksonville and reaching down in a southwestern diagonal through Orlando and Tampa to Ft. Myers), the Courts are discussing suspending all civil trials.  So, don't expect the usual prompt service from the Federal Courts. 

The bankruptcy courts are also preparing to reduce operations due to lack of funding.  Similarly, the Federal Trade Commission which, among other things, enforces the Federal Trade Commission Act and in particular the section pertaining to unfair and deceptive trade practices, has essentially shut down and sought to idle the matters it is working on in the courts.  You should expect similar slow-downs and closures from other adjudicating and enforcing bodies.

Florida state courts, while not closed, are facing budgetary constraints and have been for some time.  Thus the Florida state courts are lagging in promptness of service.

So if you want to litigate, you'll just have to wait.