The Wiki article is short but valuable for compiling links about various maniacs that completed this and similar feats, and says:
...the inaugural Trans-American footrace which took place in 1928 starting at Legion Ascot Speedway in Los Angeles and finishing in New York City in Madison Square Garden for a distance of 3,423.5 miles. Out of the 199 runners who left Los Angeles, California on March 4, 1928 at 3:30 p.m. only 55 runners finished on May 26, 1928. The race took 84 days to run from coast to coast. It was called the Bunion Derby by the newspapers and was also held in 1929. Runners included Paul Hardrock Simpson and Andy Payne who won the event in 573 hours, 4 minutes, 34 seconds.It turns out the first fame of Route 66 was not earned by west-bound experience-seekers in the 60s, but runners almost 40 years earlier! Here is a rather limited trailer, followed by some history of the winner Andy Payne, a Cherokee farm kid who wouldn't give up:
(Some original footage here.)
Once when I was driving out of Bryce Canyon National Park, I had a brief moment of despair when I noted a national forest trailhead just a few miles from the B.C.N.P. entrance - and realized that even if I quit working and foraged, I could never, ever experience every single trail. But this soon abated. For one thing, while it's fun as hell, there are more meaningful things to do in life - and I say that not to detract from the people who accomplish much bigger crossings than my comparatively meager Trans-California project, since most of them have families and productive lives in addition to their running projects. But more importantly, I think if somehow I lived a thousand years and ran every single trail, the day I take the last step on the last trail would be a much sadder day than knowing that there would always be more out there to explore on the spinning mote in the corner of the universe we've made our home.