This seems to be very location-dependent. Most states will be reasonably generous and extend Medicaid coverage to you. Some will not. Even when you have Medicaid coverage, it's still a crap-shoot whether a Dr. will take you on as a patient. Hospitals will, in general, but there's plenty of Dr's offices with "No Medicaid" signs in them.
COBRA is an utter joke. If you've just lost your job, how are you supposed to afford $1750/month [1] for medical insurance for your family ?
I think Obamacare was a step in the right direction for health-care in the US. I think it's woefully short of just about anywhere in Europe. The entire healthcare industry in the US seems to pile on huge amounts of stress right at the point where you need to just get well. In-network/Out-of-network, covered/non-covered, co-pays, crazy-high deductibles, the works. In the UK, the only thing I worry about paying for is parking at the hospital...
[1]:https://www.brookings.edu/blog/usc-brookings-schaeffer-on-he...