Co Springs to LA by way of Vegas? I suppose there's some cool spots along the way, but that's going to primarily be a traditional road tour. It would be pretty tricky to fold in everything from singletrack to loooooong stretches of tarmac on anything but a mountain bike fitted with light panniers.
For stretches of pavement like you would encounter, the ideal platform is a proper road touring bike, but that would rule out any singletrack. The best platform for singletrack is without question a mountain bike of some flavor, but that isn't always the most effecient for riding a thousand miles of road shoulder. I think you'll have to make a pretty serious comprimise if you want to do it all.
One thing is for certain, once you get to Durango or Grand Junction, your singletrack options westward are near zero outside of a couple sections here and there.