Do you need a place to stay tonight? Can you get downtown to catch one of the RTD buses that comes up here? I could drive you back down in the morning.
Isn't travel fun? I guess if you can't find a hotel room your best bet is to head to the airport and see if you can fly standby. I have had some "success" with this strategy although sometimes it means you have to fly to Phoenix to catch a flight back to Grand Junction.
Not in the mood to spend more time hanging around the airport in the hope of catching a standby flight? You might try some of the hotels and motels along the I-70 corridor out to the west of Denver or see if there are any rooms available in downtown Denver proper.
For me the break point is who is footing the bill, if I'm paying for the trip then I'll hang out at the airport until I can get on the next flight to somewhere that connects to where I want to go. If my company is footing the bill I'll normally find a hotel room some place close or at least convenient to the airport. For high priority jobs when Customers are waiting on me to show up at their facility I have rented a car and driven the distance between where I was and the Customer's facility.
There are almost always options to get yourself where you want to go, be sure to eat at normal intervals and keep a positive attitude (it sounds stupid but it makes a big difference). Take a few seconds to explain your plight to airline agents, hotel clerks, and any one else who is in a position to help you. Sometimes you get lucky and people will step up and help you out or at least point you in the right direction.
I won't bore you with the details but I spent four days and nights in the Orlando airport during and after hurricane Charley in 2004. Obviously I got home eventually but it took some doing and some mental and physical endurance.
I can explain it to you but I can't understand it for you.
"Any man who thinks he can be happy and prosperous by letting the Government take care of him; better take a closer look at the American Indian." - Henry Ford
Corruptissima re publica plurimae leges; When the Republic is at its most corrupt the laws are most numerous. - Publius Cornelius Tacitus