A few months at best

It's the lack of vitamins that gets you.

Vitamin C deficiency is known colloquially as scurvy and was one of the biggest killers of sailors in the age of exploration.

Simply, you need your fruit and veg or you're going to die.

You can get around this if you have supplies of concentrated fruit juice or vitamin supplement pills, but you've got to have those vitamins.

The medical term is kwashiorkor.

It was first identified in Africa in 1935. Mothers would stop breast-feeding their child when they became pregnant again. The older children would get plenty of calories from a high-carbohydrate diet, but were no longer getting protein (from the breast milk). The name "kwashiorkor" is a word in Ga which means "the sickness the baby gets when the new baby comes".

Signs and symptoms include:

• lower immune response, thinning hair, and tooth loss. These all rely on proteins.


• muscle breakdown. This includes both skeletal muscle and the respiratory diaphragm. The body reclaims proteins, which are broken down into amino acids that are released into the blood.


• increase in blood urea nitrogen. Amino acids are converted into glucose in the liver, by removing the nitrogen.


• fat deposits in the liver. The high carbohydrate diet actually encourages the liver to store the excess carbohydrate as fat.


• liver failure. With less protein to work with, the liver cells shrink and get replaced by the fat deposits.


• reduced blood proteins. Albumin and clotting factors are proteins that are normally made in the liver.


• swelling (edema), particularly in the ankles and feet. Reduced albumin draws water into cells by osmosis, and tissues swell.


• low blood volume. The fluid has shifted to other spaces.


• distended abdomen. The enlarged fatty liver and edema in the abdomen (ascites) pushes out the abdomen, which the weakened diaphragm cannot hold in.


• rashes.


• irritability.

The amount of time depends on the person's protein reserve. Children are more commonly affected than adults, because they have fewer protein reserves. Children can die in a matter of weeks. Adults can often continue for several months.

Even if you have vitamin supplements stored, lack of fats will kill you before lack of protein. There's a phenomenon called "rabbit starvation" -- someone surviving in the wild whose only meat is wild rabbits will die in a few months because there isn't enough fat in the meat -- some vitamins are fat soluble and can't be absorbed, even with adequate vegetation in the diet, without enough fat intake.

Protein catabolism is a genuine issue: it's why people in WWII concentration camp photos look like living skeletons; their bodies have metabolized their own muscle to keep their brains and organs running. But if you have zero fat in a calorie-sufficient diet, you'll still waste and die even if there's enough protein to avoid digesting your own muscles.

I question the premise of the question.

In most places where you can find dry grains and pasta, you can also find dry (and canned) beans, lentils, peas, soya, chickpeas, nuts, etc. Combining those with grains will give you a complete protein containing all the essential amino acids needed to sustain the human body. These pulses can, similarly to rice, last for many years if stored away from moisture in airtight conditions away from sunlight. Hermetic food can also be kept for a very, very long time.

Indeed, the vitamins are a bigger worry. Your heroes need either hermetic juices, hermetic fruits/vegetables (and even milk or eggs, for B12) or dietary supplements.

Also, I would like to point out that grains are not "pure carbs". Even white rice contains 2.6% protein. Pasta (from wheat, unenriched), has 5.8%. Oats contain 16.9%. Moreover, these proteins consist of amino acid residues. Your heroes will need both them, and the protein from legumes. If they only were to eat beans, for example, they would also get deficiency. Both grains and legumes are needed to get a complete protein. Some notable exceptions to this are the soya bean, amaranth, chia and quinoa, which are complete proteins in themselves.

Hermetic eggs, meat or dairy are also options for getting protein, however, I suspect such products may be in a shorter supply in an apocalypse situation.

I think as long as your heroes know a little bit about the basics of nutrition, they should be able to dodge protein deficiency.

White rice, flour, pasta, and popcorn are not pure carbs. Rice has about 8% of its calories from protein. Flour is about 11%, pasta about 14% and popcorn about 12%.

It's recommended you get at least 10% of your calories from protein (about 0.8g/kg body weight). This is not the bare minimum required for survival; it's a recommendation. These grains should be sufficient in this regard.

These grains alone do not have all the essential amino acids (wheat, for instance, is deficient in lysine). However, when combined with lentils or other pulses, legumes or seeds, you can get all the essential amino acids. Dried lentils and pulses have long shelf lives.

The remaining necessities are all things you need in small amounts: vitamins, minerals, omega-3 fatty acids, salt, etc. Salt, of course, doesn't expire. For the others, I would raid a pharmacy or supermarket for supplements.

If we assume nothing but carbs (e.g. white rice), they'll have salt/electrolyte problems before lack of fat or vitamins fells them. But if we must add only from the snacks, the right candy may make all the difference!

In the reducto-ad-carbohydrate case of white rice and nothing else, the lack of salt and related electrolytes will cause significant health problems within a week -- well before lack of fat or vitamins A - D become issues. So salt is a priority; ditto Potassium, Magnesium in short order. (Salt + Salt substitute.)

But what about the junk food; can it significantly help this poor diet?
If they get to choose just one junk-food thing to add to this 'diet,' what's a good choice?

Candy, especially chocolate/peanut-based candies: Reese's PB cups, peanut M&Ms, Mr. Goodbar. Fat from both chocolate and the peanuts, a little salt in most candy, some protein from the peanuts, maybe a trace of fat-soluble vitamins A and D. A trail mix heavy in salted peanuts and raisins would also work pretty well, assuming that's sufficiently junky. Most chips/crisps will provide fat and salt, but not much protein.

Do I want to eat this diet? No. But If I had to supplement a ton of white rice with a single junk-food choice, I'd go for the peanut M&Ms. Thence multi-vitamin pills.

Not a problem.

There are literally food sources all around us. The only way your survivors would have to survive on "junk food" is if they were somehow trapped in an industrial city or in the middle of a desert, and even then they would learn to find alternate sources of food as part of surviving. If it's a situation where they have adequate clean water, they'll be able to find edibles.

Once they manage to get into the country, they should very quickly find other survivors who actually know how to grow food and/or have a rough understanding of which wild foods are good to eat. Heck, they'll find good food literally growing on trees or out of the ground, if they come upon an orchard or a cabbage farm.

To summarize some of the other answers: the survivors will need to combine dried grains, dried legumes, jarred/canned fats, and canned fruits & veggies to get a complete daily meal, reserving the more limited supplies of canned meat for holidays. The many bottles of vitamins & minerals on drugstore shelves should shore up deficiencies for some time to come, while the survivors learn to turn city lots into truck gardens. (I hope someone knows about crop rotation!)

There's two big problems with the "oh, it's easy" solution outlined above. One is adequate storage conditions. I was born before common A/C in the US's Upper Midwest, so I know that in most locations food would have to be moved to long-term storage in a basement, or it will go rancid quite quickly. How much gets moved puts an upper limit on the food available a year after the Disaster.

This leads to the second big problem: hoarding. People don't have to hoard the entire store, just one key item in the complex set of ingredients above, to create a famine in a land of plenty. (As famines in our world often occur.) Most likely, the clever hoarders who stock up on fats (especially, yes, chocolate) will be the ones who find themselves both wealthy and hated. Government will be essential!

Canned Food

Ignore the expiration dates. Canned food lasts for decades.

My grandfather was an American soldier during the Korean War. Due to his special dietary requirements, he survived on food left over from WWII. Crackers stored in plastic in sealed boxes lasted (due to their low water contented.) Canned fish also lasted that long.

This article, quoting the US FSIS says that canned foods can be safe indefinitely.

Vitamins

Modern stores are loaded with nutritional supplements. Again ignoring expiration dates, dry vitamin capsules can last at least a decade. Even if it degrades somewhat, there should be plenty to keep the survivors from deficiency.

Between the two, there will be adequate nutrition for your survivors for at least a decade or until they run out of supplies.