Teeny,
Do you work for Kaiser or just have kaiser insurance?
You can certainly carry COBRA insurance until your coverage with your new jobs kicks in. COBRA is expensive. I believe you have to pay 100% of insurance cost + 2% for administrative fee. (so if your employer currently contributes, it can be a shock)
I see you are in California, so you can get "covered California" insurance, which is basically "obamacare" insurance, again I think it is expensive, but at least it is coverage.