Williams, of West Harford, Conn., runs about 25 miles a day on his trek, which he has dreamed of since seeing the movie's title character run across the continent.
"I saw that movie in high school," he told The Early Show co-anchor Julie Chen, "and I just kinda fell in love with the idea. …To me, it was an amazing display of freedom, athleticism and willpower that he could just kinda pick up and do that. So I just I said to myself, 'Man, that's something I want to do some day!' "
"Why settle for just having a job and getting married?" Williams asked, when questioned by The Associated Press about his motivation. "Why not just do something different? Why not just live?"
Asked by Chen what his average day is like, Williams responded, "Basically, I wake up sometime between 6 and 7. I try to leave between 8 and 9. I average about, probably, 30 miles a day. My longest day is 56, though, actually. I was in Missouri somewhere. That was pretty killer.
"I'm not running every day," he continued. "I'll take days off. Like when I get to a city, sometimes I take a day off, and I'd say my longest day, my longest stretch, has been nine days on, and sometimes I'll take two days off. A day off here, a day off there. Something like that."
Williams showed Chen the baby stroller he uses to carry his gear: "This is a great idea. Actually, I got this idea from two guys who did the cross-country run from New Jersey to Oregon, Dave and Scott. And they used a baby jogger. So that's what I decided to use as well.
"Basically, it's got my tent in it. …I've got a spare tire. My backpack. I got, you know, a sleeping bag in there. A little blowup mattress. It's kind of stacked with basically everything I need."
Williams' girlfriend, Sara Hubeny of New Haven, Conn., is tracking his trip.
"Think outside the box, think positive, and do something," is the motto posted on Williams' Web site, where his friends post encouraging messages.
The Web site, runwillyrun.com, is based on his nickname and the line from the movie in which Gump's girlfriend implores him to "Run, Forrest, run!"
Williams, 26, weighs 149 pounds, about 10 pounds less than when he started in May on the 3,100-mile journey. He expects to finish on Sept. 10.