How likely to get last-minute spots in national parks

For the Tetons Gros Morne is an easy one. They have a few sites with power but the vast majority are dry. Stayed there over a July 4th weekend a few years back. It was full only for the July 3rd night. Very surprised. I had made reservations early for the 2nd through 5th, thinking there would be big demand. I was very wrong, even with my relatively large 5er.