Or Should I Traverse the Rockies

I've been studying maps in order to finalize the trail for the trek next summer from the Arch to Tor House. I'm sure that the first half will be from the Arch to La Junta, Colorado. An alternative route, rather than cutting south to Albuquerque and then heading west to Tor House, would be to continue biking from La Junta to Pueblo, Colorado, where I could sell or donate my bike, then hike along HWY 50 through the Rockies, ending up in Utah, where I would rejoin the American Discovery Trail. The question is this: Could I traverse the Rockies through Colorado on foot? Ann says the mountains would be too steep to climb on a bike, and coming down a 12,000 foot mountain would likely result in a disastrous wreck. But HWY 50 looks as if it mostly follows along the base of the Rockies. Maybe I need elevation maps? But traversing the Rockies, by bike or foot, would be cool.