Michael Gibson you need to first off learn your State's landlord / tenant laws. In most states you need to mitigate your damages. So when they move out, the tenant is still responsible for paying the rent. You, as the landlord, are suppose to try and rent the place. Once the unit is rented their obligation ends.
I actually have a $500 "break the lease" fee plus reasonable advertising expenses in addition to them being responsible for the rent. Realistically you probably won't get rent from your tenant after they move out. Yes you can take them to small claims court but good luck collecting a judgement.
Hopefully you are charging them a late fee every month. One last thing and I hope you take this the right way. The tenant is threatening you with a lawsuit if you don't let them break the lease and give their security deposit back? I would explain to them in shall we say, not so nice of terms that you are the boss of the rental. Tell them you will not take their threats - this is a business and not a hobby! It's tough at first to take this type of attitude with a tenant but after you get screwed enough, you'll get your authoritative face on. Good luck!