Without the vaccine, I don't think it would have been 2M within 2 years, although it might have hit there eventually given area under the curve.
And honestly I don't know that it would have been 2M anyway.
I believe that was based on over 200M Americans getting the virus over that time, and thus slightly above 1% IFR. Based on estimates of unreported infections to confirmed cases, that seems to be a high assumption for IFR. I think it's probably a little above half that, maybe in the 0.5-0.6% range.
Maybe if all 330M residents of the United States got it, at an IFR close to 0.6%, you'd approach 2M, but herd immunity might stop the spread before everyone got it.