We've taken the Auto Train to Sanford FL many times, the Silver Star to Orlando, and many regional trips to NYC and such. Really excited to head west!
Heading west it's a little over 51 hours on that route, 65 hours heading east. As always with Amtrak, delays are to be expected and built into the traveler's schedule. It's not the way to travel if you're inpatient or in a hurry, but if you're in a total relax vibe like we'll be you can't beat it.
We'll be heading nearly due west through Denver as Bubbler mentioned and reaching the west coast near San Francisco. It'll take us a week to get there as we're stopping several places along the way. Spending a week in California and then heading east out of LA across the deep south before turning north along the Mississippi towards Chicagoland.