As you might imagine, a chair chosen by the President to his bad back is a very good quality chair - both durable and very comfortable. It has a nicely contoured seat and back, smooth rounded thick posts, and long runners that enable you to find a comfortable recline position. The back post is steam bent to give it additional angle, which is a very nice and fairly rare feature. I have sat in these rockers and they are very comfortable. I do not think they are comfortable as the Independence Rocker which I blogged about earlier, but for a rocker with a woven seat and back (which necessitates less contour for manufacturing reasons), it's pretty nice..
The chair is still available today. It's official name is the "Carolina Rocker" but it has always been nicknamed "The Kennedy Rocker" or the "Presidential Rocker" ever since JFK discovered them. Here is another excellent website with the story of the original Kennedy Rocker.