I had a scary density altitude moment today in my 1973 Cessna 172M and am parsing and searching and thinking about an upgrade. The cost of a 177 to own and fly are quite a bit less, but I worry about my capacity... I would like to be able to carry 4 adults with luggage.
What happened? DA sneaks up on everyone who doesn't fly at high DA airports and has to do the calculations for every takeoff. If you're going to do a lot more high DA flying, start making takeoff distance calculations for every takeoff, easiest way is an app on any smart-phone, or a quick use of a chart or table from the POH.
For four adults with baggage you're really looking at a 182 or a 206 if you're staying with Cessna. A 172 is really a 2+2 at higher density altitudes unless you leave the tanks half-empty. Even then most Mountain CFIs won't launch West out of Denver in a Skyhawk after about 9 AM in the summer. Preferably earlier. They also want to burn down fuel load and stay light.
Temperature makes a HUGE difference. If you can modify your behavior to be off the ground by 7 AM a Skyhawk can be a Mountain airplane.
But not with four adults. I wouldn't even launch my Skylane into the Mountains without leaving some fuel behind with four adults and bags. CAP around here only fuels to the tabs in the T182T and three crew and a survival kit hits max gross regularly.
The 177 really isn't that great a climber. It's a faster Skyhawk that will travel better but it'd be no better in the mountains. To really utilize either one in mountains you're going to have to practice and get good at finding ridge lift, thermals, etc. You're a powered glider pilot in a Skyhawk with two plus bags. Four flat-landers in a Skyhawk is quite often the subject of SAR activity and fatalities west of DEN. Or at least it used to be a regular multiple time summer occurrence when more people were flying in the early 90s.
The ultimate "fix" for most aircraft going West of DEN into the really high DA is turbocharging. You're still going to chew up a lot of runway but at least you have sea-level power to accelerate. At Leadville last summer my Skylane's engine was putting out about 65% of rated HP for takeoff and we felt it. We had two bigger than FAA standard people and half tanks on our long-range (80 gal/75 useable) tanks.
How high were you and how hot was it outside? Remember back to your Dry Adiabatic lapse rate and realize also that 70F might be "hot" when normal atmospheric conditions mean that you should subtract 3F per 1000' of altitude to compare apples to apples.
( Just a goof on Anthony) By chance is your 172 one of the older models with the 145hp Conti O-300?
- Leadville does flight instruction in normally aspirated 150hp 172's. 
