Obamacare is just a means to an end, not an end in itself. The real goal is a gov't-run healthcare system. Barney Frank, an architect of Obamacare, admitted that in a 2009 interview:
Because we don’t have the votes for it. I wish we did. I think if we get a good public option that could lead to single-payer and that’s the best way to reach single-payer.
He didn't quite explain how Obamacare is transitional to a single-payer system. One possibility is that it's a softening-up exercise. It prepares the public for a single-payer system.
There is, however, a more cynical theory. That Obamacare was designed to destroy private healthcare by producing a death spiral in the private insurance market. Here's a description:
Obamacare’s community rating results in insurance prices that are higher for younger people than they would be in a free market, and its guaranteed issue allows people to sign up for insurance even if they get sick, so young and healthy people have ample incentive to forgo insurance. This leaves the insurance “risk pool” older and sicker and, hence, more costly to insure. Premiums will have to rise to cover those costs, leading some of the younger and healthier people who did initially sign up to then drop out. The risk pool then becomes even older and sicker, premiums rise again, and the process repeats.
Now, why do I bring this up? There's a tradition of doctor/patient confidentiality, as well as doctor/patient privilege. But a single-payer system will erase the doctor/patient confidentiality/privilege? To begin with, if physicians are actually gov't employees, then your medical records are gov't records. Even if technically, only a subset of gov't employees has access to the records, there is no real doctor/patient confidentiality. Also, it's trivially easy for "confidential" records to be accessed by unauthorized personnel.
And even if the physicians don't work directly for the gov't, if many of the treatments require authorization by some gov't bureaucrat, then once again, there will be a gov't record of the patient's condition and treatment.
Perhaps a parallel objection might be raised with respect to physicians who must request authorization from a private health insurance company. That's a problem, but that's still different from the gov't knowing all about your sensitive medical conditions.
Also, Americans didn't always have health insurance. That's not a given.