> there just aren't enough people to sustain two months' growth
It can be simply calculated: it is expected that without measures the growth to 70% of population would be continuous (very approximately, the end phase wouldn't, we're estimating the limit). So the target is 6e9 people. If we assume that 4/5ths are the people who remain undetected by our current sampling, we want to know the growth between the current known infected and the target which is then 1.26e9 people. Currently known are 0.5 million infected. So the fastest end of growth phase would be just: 2520 times or around 2^11=2048 == just 11 times 3 day doubling time, or 33 days.
The growth will surely not be always exactly 3 days however, so it will be slower, but still not less dramatic, because the resources are many, many times smaller, in the poorer countries many tens of times smaller.
In short it can be very, very bad, and that will be much longer than just a month, just not the exact growth as now.
See the papers from Imperial College London for the exact shapes of the curves and the examples of their speed and growth.
> Nobody has thousandfold more hospital beds and doctors ready, even less a million times more, which is the two month's growth.
And in a few additional months, we will need more ICU beds than the number of atoms in the universe.
Infection rates are already significant, there just aren't enough people to sustain two months' growth.