This interactive graph shows the quantity of icu and other beds, and ventilators needed and available for the US and for all 50 states over time.
https://covid19.healthdata.org/projections
I love that site, but given the stories I'm hearing from friends, their methods are a little bit off, because I think they are not taking into account how long it takes to get a test result back. This is how I do it:
On March 25 (last Wed), we had 1,127 cases in PA. That is the number of people who tested positive. In order to test positive, you need to show symptoms, which takes a week. According to friends on FB who have taken the test, and probably have Coronavirus right now, it takes roughly a week to get a test result back from a drive through testing site. Some say longer, some say shorter. I think you get results faster in Pittsburgh and Philly, for example. I'm just going to use a rough estimate of a week for results. That's on top of the week it takes to show symptoms and get approval to be tested.
Keep in mind, I'm only interested in undiagnosed cases that are out there spreading Coronavirus. So I go back two weeks, and subtract the 15 cases we had on March 11, because those cases have already spread it and are factored into the current numbers. That leaves us with 1112 cases.
I kinda eyeballed the doubling rate to be 2.5 days. So we are going back two weeks, rather than one week, as the healthdata.org site seems to do, and doubling 1112 cases 5.6 times to get to the number of undiagnosed cases last Wed.
That gives me 56,935 cases that will be diagnosed by April 8 (next Wed).
My chart from this projection shows that we will have 4,448 cases yesterday. We actually had 4,087 cases. So I am off by 361 cases, but all things considered, I'm definitely in the ballpark.
This forecast predicts 18k corona cases on Saturday. On Saturday, according to the numbers from the site you posted, we are projected to have 16k hospital beds. So I'm guessing sommetime this coming weekend we will cross the line where we have more Coronavirus cases than beds.
I second guessed this method quite a bit when I first ran the numbers, as any good economist does when they forecast (my degree is in economics). It's almost a week later, and the numbers seem to be keeping up with the forecast relatively well, so my confidence in it is much higher now, unfortunately.
Source on COVID19 numbers in Pennsylvania.