South Korea's mortality rate is 2.5 ±0.4%...
The U.S. currently has 678,210 known infections...
If we (optimistically!) assume that our true COVID-19 mortality rate is as low as S. Korea's, then our 34,641 COVID-19 deaths would imply that we had actually about 34,641 / 0.025 = 1,385,640 infections some period Td of time ago, where Td is the average amount of time from infection to death, for those who die of the disease. If Td is 10 days, that would mean that on April 7 we had 1,385,640 infections.
On April 7 we had 403,531 identified cases. 1,385,640 / 403,531 = 3.434, suggesting that we had about 2.4 unidentified infections for every identified case.
If, however, we (pessimistically) assume that our our true fatality rate is 4% (i.e., closer to the current naively-calculated rate of 5.11%), and Td = 10 days, then 34,641 / 0.04 = 866,025 infections on April 7. 866,025 / 403,531 = 2.146, suggesting that we had only about 1.1 unidentified infections for every identified case.
Since (unfortunately!) the U.S. currently tests few asymptomatic individuals, and about half of the people infected are thought to be asymptomatic, it is doubtful that the number of unidentified infections could be any lower than that.
However, if Td is 14 days, rather than 10 days, then the denominator is 247,729 (the known case count on April 2). A 2.5% mortality rate yields 1,385,640 / 247,729 = 5.59, suggesting that we had 4.59 undiagnosed infections for every identified case. A 4% mortality rate yields 866,025 / 247,729 = 3.50, suggesting that we had 2.5 diagnosed infections for every identified case.
That pretty much brackets the plausible range: between 1.1 and 4.6 undiagnosed infections for every identified case. Call it 2.85 ±1.75 undiagnosed cases per known case.
Assuming that ratio has not changed in the last 10-14 days (though it's actually probably come down a bit -- at least I hope so!), then our current known case count of 678,210 suggests that our true number of infected to date is 1.4 to 3.8 million, with a mid-range guess of 2.6 million = 0.8% of the American population.