In the States everybody is so concerned about liability.... We tried to store at Hertz (where we dropped the rental); no storage facility, no luck. Try a hotel; I tried several, if you are not a guest then they are not allowed. I tried the Information Centre; no luck, they had some bad experiences.... in the past. But they could not realy help me any further. One advise: try the Greyhound Bus Center. And yes! there you can store your luggage. Even my somewhat bigger suitcase. The lockers are somewhat small but high and deep enough. First 3 hours is to be paid for; $ 3 and after that a dollar for an extra hour.
There is a luggage storage service a short one minute walk from Union Station in downtown Denver - LUGDEN. You can make a reservation online - lugden.com, call - (303) 747-5600, or show up as a walk-in. They offer hourly, day, overnight and weekly bag storage. Great place to store your luggage if you're on a layover from Denver International Airport, or going to a concert, or headed to a Rockies game at Coors field and want to enjoy yourself without having to lug your bags around.