This is simply false. By forcing new buyers into the insurance market, and penalizing them if they do not enter that market, Obamacare affects demand. And where there is additional demand for a finite resource, prices increase (which in fact has happened steadily since Obamacare debuted).
It does not "lower the price curve" because people who were not using health care services before are using them now -- this drives prices UP, not DOWN, and anyone would predict after a first-level economics course. Even without that prediction, simple observation would show you that, right now today, the mechanism is increasing prices. "Eventually" ? Yes, a bar I used to go to had a sign on the backbar offering "Free beer tomorrow." Tomorrow is always a day away.