The Democrats kept watering the ACA down to try and get the Republicans on board.  It went something like this:
Democrats: Hey, so you don't like single payer, but you liked the idea of an individual mandate, so how about that.
Republicans: sure
Democrats: so, we took out single payer and added the mandate, can we count on your votes?
Republicans: Nope
This went on and on.  So the lie that the Rs had no hand in it is exactly that a lie, just one more in a long series of them about the ACA.