Am I able to break my lease without incurring HUGE fees?

We have been in this apartment since August of 2010, and are close to our lease being done. But since day one of moving in this place, we noticed cockroach's in our apartment. I scrubbed and cleaned and I was assured by the office that they would be taken care of and be gone. I have 4 young children (7 months, 19 months, 3 and 5) and I am concerned for their health living here. I know it can make them very ill and I can't stand the idea of maybe one of them crawling on one of my children. We are very clean people, and there are never any dishes left out in the sink. I do my best to be sure it is extremely clean within this apartment. Does anyone know if we can break this lease and move out without having to pay HUGE amount of money for early termination? We live in FL if that helps.