I've made the drive on I-70 from Denver to Vail and Breckenridge a couple of times. That's a solid 2 hour drive and it's not even halfway to Grand Junction. If you make that drive I'd plan on at least 5 hours, and that's if it's not snowing.
They keep the interstate pretty well groomed, but that time of year you are just as likely to have weather in the 50's and 60's as you are a foot of snow. The weather is crazy out there.
Another option would be to fly to Eagle Airport in Vail (EGE) and drive from there. That would shave 2-3 hours off of your drive and still give you a chance to drive through some of the scenic areas.