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My mapping program shows that it's 1634 miles, and that's a FULL 3 days drive via I-74/I-80. In order to do that in 24 hours, you would have to AVERAGE 68 mph. This is totally unrealistic - computers never have to stop for anything and are never delayed by any kind of traffic or construction.

If you want to do anything more than just drive on Interstates and sightsee only through the windshield, you need to add more time.

Between Cincy and either Denver or Cheyenne, there is absolutely nothing that would make I-70 any more interesting than I-80. However, from Denver west along a few different routes, the drive is a lot more enjoyable, and I wouldn't do it without at least a 4th day to play with.

It's quite reasonable to spend the first night near either Des Moines or Kansas City, and the second night near either Denver or Cheyenne.

What I'd personally do is take a 4th day and do some serious sightseeing in Colorado. Take either I-74 to Indy to I-70, or I-71 to Louisville, then I-64 to I-70 - to US-24 to Colorado Springs. Attractions there are the Garden of the Gods and Pikes Peak. Then head up I-24 to Loveland and take US-34 through Rocky Mountain National Park to Granby, then US-40 to Steamboat Springs - a very nice place to spend the night.