I changed your practice area form Criminal Law to Child Support. I think you will get more relevant responses under that practice area.
Best of luck.
The above is not intended as legal advice. The response does not constitute the creation of an attorney client relationship as this forum does not provide for a confidential communication.
I take it that he lives in New Jersey, and that you have used the State of New Jersey to attempt to collect support in the past. Now that you live in Florida, you've contacted the Child Support Enforcement Division of the Florida Department of Revenue. If your daughter's father still lives in New Jersey, the State of Florida will just send your case to the State of New Jersey.
Under Florida law, social security checks can't normally be garnished, but social security can be garnished for child support. New Jersey law may be different. You should probably contact a New Jersey lawyer. You'll probably have better results using a private lawyer than using the state. Plus, you can learn if his social security can be garnished there.
The contents of this answer should be considered friendly advice, not legal advice (I'm a pretty friendly guy), and the answer should not be construed to constitute an attorney-client relationship. If you'd like actual legal advice, call me for a free consultation at 813-635-0222. Also, if you liked this answer as much as my big ego thinks you did, be sure to click the thumbs-up button!