No, you can't sue, and you don't get anything. What you can do is report them to the FL Dept of Labor if they are in violation of the law, and the Dept of Labor may fine the employer, force them to comply, and even shut down their business if they fail to comply.

To add to Sarah Grosse's response, I do not know of any law that the employer would be in violation of - neither federal nor Florida law requires that employers provide meal breaks or breaks of any kind (contrary to popular belief). So, your only rights would come from either the company's own policy on breaks, or a contract - either individual or a labor contract, if there is one. (The law provides when breaks must be paid for, if they are given - but not that they must be given. True meal breaks, as opposed to short rest breaks for hourly personnel (non-exempt), do not need to be paid.)

However, something does not sound right here. I have never heard of a company that does not allow for meal breaks. Are you saying that the breaks are not paid? Or that there is so much work you are always interrupted although you get a break? Or is your job unusual in some way such that meals must be eaten on the run so that you are always available for work?

If there is more to this story, then you might want to re-post with more facts. Otherwise, your question indicates that you are not happy at work. Although everyone who has a job these days should be careful about jeopardizing their income, you of course are free to look for work elsewhere if you don't like your company. But if the compensation and/or benefits are reasonable, give some serious thought to whether you really have good reason to be disgruntled, especially in this economy. Good luck.