From the source of a coworkers wife who is working with one of the big name researchers on this at UNC, I agree with
@Chuckman of April 24th to May 4th for our peak. The peak in NC is predicted to occur later than the nation as a whole.
The problem is that it's an exponential growth. Exponential functions aren't something people are used to thinking in terms of. They start out, and remain, really slow for a long period of time and then suddenly take off like mad.
I have used the following analogy in a few threads, but it really does illustrate the principle. If you have a pond with a lily pad and the pad(s) double each day and it takes 48 days to completely cover the pond, how many days to cover half of it? I asked my dad this question yesterday and he said 24, which is incorrect. The correct answer is 47 days. In fact, if you go back one week from being fully covered you will have less than 1% of the pond covered. It's a 2^(x) function - and in 7 days 2^7 is 128 meaning you have 1/128th the number as of a week prior. Likewise with a pond where the lily pads double every day at day 48 you have 2.81x10^14 (think of it as 281,475 x 1 billion), which is a lot of lily pads, but back at day 10 you only have 1028 lily pads.
In terms of the corona virus, everything we can do to reduce the number of others that each person infects is like reducing the 2 in the 2^x lily pad problem. Lets say for example we reduce it to 1.5 If we did that, at 48 days we would have 283,387,333 lilypads or in rough number one-one-millionth of the number of lily pads. By reducing the spread each infected person contributes, even a little bit, the net result is a dramatic decrease.
Being an exponential function, any reaction at the start is going to seem like a supreme over reaction. At the end it is going to seem like an absurd under reaction.