My current lease ends on 12/2010. However, I signed an additional lease that runs from 1/2011 to 6/2011. I am relocating and want to give notice on the second portion of the lease that was originally signed on 1/2010 (1 year before the actual start date).

Sorry if you signed a lease extension or renewal you are bound to it. And Florida is the worst state to try and break a lease since the landlord does not have to try and find someone else.

You have three choices:
1) negotiate a buyout
2) sublet
3) find a replacement tenant

Agreed, Florida is the worst state for this to have happened in.
I would start by going to see the landlord and trying to work out an agreement that you can live with.

Thanks for the info...