Once you resign, your employer must notify INS immediately about your status change by law. Officially, there is no grace period for H1b, but practically you have to leave US within 10 day. More than 10 days will definitely have negative impact on your next visa application.
It's impossible for you to come back with H1b again although you still have "valid" visa since your status change will be in INS computer system as soon as your employer notify INS.