Dear Broke, You are asking a more important question than you may know. If you are trying to find out whether you can have a public defender for a child support hearing, you must know that you might be found in contempt of court. And Florida judges routinely order jail time for contempt of court for failing to pay court ordered child support. But, contempt of court, by definition must be willful. If you do not have the ability to pay then it isn't contempt. But, persuading the judge may be a different matter entirely.
For more detailed explanation, please read the following article:
"Case in Brief: Courts Uphold Criminal Penalties for the Failure to Pay Child Support" by Teresa A. Myers