Yes, but not so soon: at the moment in most of the places it grows exponentially, the numbers doubling every three to four days. So "and will probably get ther

Yes, but not so soon: at the moment in most of the places it grows exponentially, the numbers doubling every three to four days. So "and will probably get there in another week or so" is probably too slow. If it's really 2000 deaths per day now, I can safely estimate 4000 deaths per day in just three to four days. Then in next 4 days it will be 8000. Save this estimate and compare. In order for the effect you describe to happen (the maximum to be reached) the most popular estimate is that the number of infected has to reach around 70% of the population. Until that point the doubling of deaths every few days, without the measures to prevent that, would continue, deaths happening in always bigger amounts, but concentrated in the few weeks.