Romneycare was what the basic concept of the ACA was called before it was called Obamacare. There are very few American politicians on either side of the aisle who favour single-payer healthcare.

After Obama campaigned on healthcare as a key issue, he ended up using a Republican healthcare reform as the framework for his federal reform in order to get the corporate crony faction of the Democrat party on side. The Republicans, in a classic example of American politics being literally the dumbest thing ever, decided that they couldn’t be seen as agreeing with a Democrat (particularly a black one), even if it was their own idea, so they moved the Overton Window even further right and began claiming that even ACA was a bridge too far.