"Obamacare" isn't health insurance - it's the Affordable Care Act - it's the law that says your insurance company has to cover certain things, and can't deny you, or raise your rates due to a preexisting condition.  The law also set up a marketplace exchange where you can shop for insurance from most major insurance providers, BUT, if your income is within a certain range, you get a subsidy to pay for your premiums.  As a self-employed person, I don't know WHY you would turn down the opportunity to get lower rates for the SAME coverage as if you had bought it straight from the provider.

www.healthcare.gov   (it won't let me post a link)