Be careful about this assumption if you are working at a small startup. I recently changed jobs and was not eligible for health insurance for the first month in my new job. I thought "Oh, that's fine. I'll just pay for a month of COBRA coverage." When I went to apply I was told that COBRA only applied to companies with at least 20 employees and that I should use my state's equivalent of COBRA instead. When I went to apply for that I was told that it applies to all companies, but it is not available to people who leave their job voluntarily.
I ended up having to get a short term individual insurance plan instead. It's a bit of a risk because if a major issue related to a pre-existing condition flared up, I would probably not be covered. It's my understanding that when the new health care laws take effect next year, it will help absolve much of the risk that comes from using an individual insurance plan.