If I Get Laid Off From My Job, Can I Break My Lease Without Paying?

Know you can't. You need to look into tenants vs. Landlord rights for the do's and dont's.

Typically, no, but you can talk to your landlord and see what sort of deal you can work out.  
Expect to lose your security deposit, and possibly be asked to pay 2 months more rent.
Look at your lease agreement, there is usually a clause that will address early termination of a lease.
The only ways to get out of a lease early without penalty is if you are shipped out on orders from the armed forces, or if you happen to pass away! LOL

You shouldn't break the lease. Go to your landlord and tell him about you beening laid off. He might can help you, or you can lived off the security in most places.