850 miles is just too far for one day...
Hello again:
Getting back to that marathon drive from St. Louis to Denver: as a general rule of thumb, you should always add at least 20% to whatever fantasy time Google assigns to a drive between two points. That allows for fuel stops, bio breaks, traffic (slow trucks!), and a very brief lunch stop. By that calculation, the 12.5 hour drive, which is already much too long, becomes a 15 hour drive, just as Dave said, and that's not just exhausting, it's dangerous! Please take us seriously when we say this: fatigue is a killer, and even if it doesn't kill you literally, it'll take a toll on you physically, and it's just really not worth the time you save by not stopping in between the two cities.
The smart move here is to take a more casual pace. Get a decent nights' sleep in St. Louis; leave there at a more reasonable time of morning, and head west. Hays, Kansas is a bit over 500 miles, which is really plenty for one day; If you're bound and determined to push yourself, Colby, Kansas would be about 109 miles more, for a total of 620. That's the absolute MOST I would recommend--and only if you get a full nights' sleep before starting out! Either way, your second day would be a piece of cake, and you'd arrive in Denver early enough to see a thing or two.
My two cents.
Rick