How can I get out of a lease without incurring damage to my renters credit. And could they come after rent on the rest of the lease?

This is an unfortunate situation and is common in the economy.  Many landlords are willing to work with their tenants as a result of job loss.  I suggest having a face to face with the porperty manager/landlord and discussing the situation and provide him with a plan of your ability to start making payments again when you secure new employment.  You may be able to put something in writing saying that you can get a few months free and then begin paying at a new reduced rate.  you never know unless you ask.  If you walk away without paying the landlord can sue you and if he gets a judgment it will affect your credit.  Make the phone call to set up the meeting.  If you want to move, ask to pay a reduced rate to get out of the lease, unless the lease has a provision for that.