Stupid question, I know: could Obama order that Medicare be opened to insure those who pay for it?

It sets a price and providers can take it or leave it. But they need to set a price that most will take, or else recipients won't get care. So it's an implicit negotiation.

Because they're bigger, they can set their price lower.

But every discussion involved Congressional action. Joe Lieberman shamefully flip-flopped on it, once being clearly in favor of expanding Medicare and then for no good reason turning against it. I thought my opinion of him by that time couldnt get any worse, but it did when he did that.

No President could just 'order' medicare to do such; that's the only 'stupid' part of your suggestion, The changes would have to be approved by Congress, so around and around we go again.

It WOULD cost money, actual services for many more means much more administration/bureaucracy, and the cost of services to many more. Spending bills have to go through Congress, and as insurance companies would be adversely affected to some extent, they would fight it tooth and nail. Again.

I think Medicare overhead is so low due to lack of need for marketing/advertising. Cuts a LOT. Don't know that they negotiate with providers; Fed gov. agency does negotiate with them for Federal Employees Health Benefits Plan.

it absolutely would require a change in law, which necessarily involves congress.

unless you're talking about a 100% outsourced concept, involving zero government employees and zero government money.
if obama can somehow get a self-funding non-profit started that simply uses the medicare concepts and prices that are already public information, then sure, that would not require congressional input.

Just like federal employees. Like ACA.