Yes, they can come after you for what's known as a deficiency judgment for any money still outstanding on your mortgage once the house has been sold at a foreclosure sale. However, they don't often do it anymore, but they still could do it.
Why not consider a "short sale" in which you sell the property to someone who wants to buy and negotiate with the bank to have them take less than the full amount of the mortgage and leave you alone afterward?
Speak to a good bankruptcy lawyer as well and see if they can help you renegotiate a new interest rate with your existing bank. That way, you may still save the house and have it at a much lower interest rate. The federal governement is offering the banks great deals to do this for people.
Instead of just giving up, find a loan modification lawyer and see what interest rate they can arrange for you. If not, you can always let it go the way you're thinking of doing anyway.
Remember, banks don't want to foreclose right now. Take advantage of that knowledge and do your best and you may be pleasantly rewarded in the long run.