If you are currently covered under a group health insurance plan through your employer you are elibible to get it through a new employer. However, if you leave your current employer and there is a gap between the time you left and when you start your new one (more than 3 months), the new employer does not have to cover you. If that is the case, you'd be better off going with your Cobra coverage if you quit your present job and when you start the new one you'll be all set.