We know where it is. It's everywhere, because huge parts of the country have given up on even trying to keep it contained.
As of today we're at about 10 million cumulative cases (a full 3% of the country's entire population), 132,000 cases per day, and the cases-per-day count doubling every 20-30 days. That's a progression that gives you millions of new cases a day just by May.
132000 cases per day, doubling every 30 days, would be about 328 million additional verified infections by the beginning of May. You may note that exceeds the total number of Americans who have not already tested positive, which gives a pretty good hint that model can't actually reflect reality for that long.
Additionally, the 10M number is the number of people who have tested positive, not the number who have been infected, which is probably several times higher than that even.
So yeah. I doubt we have even two more doublings ahead of us, at least as measured by hospitalizations (positive tests are a bad measure because early testing was very lacking). Less than one wouldn't surprise me.
Known cases. True numbers are likely to be much higher than that. For starters, the estimated percentage of entirely asymptomatic infections is around 18% to 80%(1), with many more getting only mild symptoms. Many if not most people with mild symptoms will never bother to get tested.
It would not be surprising if 100 million Americans have in fact been infected already. That's the kind of ratio of known to actual cases that antibody testing has repeatedly found. And even that may be an underestimate, as antibody testing doesn't measure T-cell response.
As of today we're at about 10 million cumulative cases (a full 3% of the country's entire population), 132,000 cases per day, and the cases-per-day count doubling every 20-30 days. That's a progression that gives you millions of new cases a day just by May.