According to Guinness World Records, as of 2009, this is the strongest spider. It has been able to resist a force 38 times its own weight when defending its trapdoor. This equates to a man trying to hold a door closed while it is being pulled on the other side by a small jet plane.(1)
Unfortunately, the Guinness book doesn't mention if it's the strongest North American spider or if it's the strongest in the world. Also, one thing to think about is whether or not every spider's strength has been measured (no, they most definitely have not). The information is flawed in many respects, but it still asserts the fact that these spiders are pretty strong.