Now that we've seen more data, it looks like roughly a 3-week lag from cases to deaths. Cases peaked a week ago, so expect deaths to peak in mid-August. Deaths are at 968 (7-day average). It's hard to say how much they'll increase in 2 weeks since testing has been going up too (although not as fast as the number of cases, which increased almost twice as fast), but I'd guess deaths will max out at around 1250 per day.
The question is how fast will that come down. In the past week, cases have come down about 4%. That means deaths from August 15 to August 22 would go down to about 1200.
In the last 2 weeks of April, NYC came down fast (50% in 2 weeks) due to fairly strict stay-at-home. With mandatory masks and other restrictions, they've been pretty flat lately, but at a low number (~700 cases per day). For comparison, Arizona has gone down 33%.... in 3 weeks. And most other states have barely ticked down or are still increasing.