Interesting topic.
I'd venture to say that many responded without really reading the OP, and the OP'ers clarification of his intent.
Rocky Mts.
Time frame is over a winter
Feeding yourself
Defense is from being eaten, not "bad guys".
Having lived in the rockies for a fairly long time, I, so far, haven't met or heard of anyone that uses a shotgun for much besides bird hunting in season. More sport shooting than meat making. Looking at the natives and bush folks up north that make a living out in the wild places, they also don't tend to rely on shotguns much besides laying in quantities of geese and ducks. The main meat guns in the rockies and up north are center fire sporter rifles, and 22's. Most natives tend towards smaller caliber centerfires, weight being a factor, not because they carry large amounts of ammo on them, but because the cost of ammo in the far away places is related to weight to ship it in to the traders. Recoil seems to be a factor also. So far, I also haven't heard of people that use their guns as a means of making a living having large quantities of ammo. Calvin Rutstrum, who wrote many books about bush living in the Canadian wilds mentions that 1 20 rd box of 30-30 shells was plenty for a winter of living and securing meat. He mentions having a .22 also at times, and felt that 1 50 rd box was plenty for a fairly long period. He was out doing it back in the early 1900's, and would make months long canoe and/or dogsled trips WAY out in the bush. He stated that overall, after trying many different calibers and guns, the 30-30 was his opinion of the best general purpose gun, as it didn't ruin (bloodshot) large amounts of meat, and it was very handy to carry, as well as reliable under all conditions. He mainly hunted deer, moose and caribou for meat and had no issues with the 30-30 for such uses. Rutstrum continued venturing into the bush and writing into the 1980s, and his thoughts on the matter were after long use and trying a number of various guns and loads.
Other writers that have made the plunge into the subsistance lifestyle, and made observations on others doing the same, tend towards the same general conclusuions, tho some prefer a scoped bolt gun in 30-06 or similar caliber, depending on the openess of the country.
I personally like to use a 30-30 with very light loads for grouse and small game, or a .22 pistol or rifle. When actually "hunting" (rather than an everyday carry gun) a scoped 30-06 does about anything you realistically need doing in the rockies. Either would do, tho I like a 45-70 for a carry gun when not "hunting" because we have a fair population of grizzlies here. I probably wouldn't choose the 45-70 if I had to go far on foot tho. People defense isn't a big issue in the wild and silent places, tho in that setting, any gun is enough for that purpose. Realistically, we are talking chance encounters with extremely rare nut cases, not the common street thugs. Street thugs don't hang out in wild places. Nowhere in the OP was end of civilization or social breakdown etc mentioned, or even hinted at. Even were such the case, out in the mountains is about the last place you would run into anyone you would need to be concerned about unsocial behaviour. Those sort of people wouldn't likely last long in the mountains, no matter what guns or how much ammo they managed to drag out there with them.
I've had less funtion problems with Winchester levers (mine are pre-64 and pre-war) than with Springfield and Mauser bolts. I've also seen several various makes of AK's fail to function for various reasons.
I've had less trouble with Smith DA's than Ruger SA's also.
YMMV