re bolded: there's an exponential growth "phase" of the sigmoidal curve, which we're in right now. Since testing is so variable and unknown, one estimate of where we are on the curve is looking at death rates in Italy/Spain/France when they went lockdown compared to today, then apply our "delayed" start of social distancing date relative to Europe's.
Italy shut down March 9 and had 366 deaths. They're at about 8,100 deaths today.
France and Spain shut down about March 14 and had 79 and 121 deaths, today at 1700 and 4000 respectively.
On March 20 (rough avg natl shut down date ?), US was at 150 deaths, 3 days later was at 340. Given the sheer size of our population, the fact that we have the most cases of any nation in the world and have started social distancing the latest relative to all other major nations with believable data, and similar association of curve to relative shut down dates, we're probably going to end up with the most absolute deaths for any country in the immediate future, and it probably won't be close.
I'm using these tables as a reference. Also not so concerned about those table wrt accuracy to the case, just looking at gross relative numbers and associated points on curve.