According to Koutsos et al (
http://www.bioone.org/doi/abs/10.1647/1 ... 5D2.0.CO;2 ), wild birds need a lot more calories than captive birds but their requirement for everything else including protein is about the same.
Carbohydrates and fat are the primary energy sources for wild birds, pet birds, humans, and just about any animal that isn't a pure carnivore. It's possible to burn protein for energy but it's the least efficient source, which means you have to eat a lot more of it to get the same amount of energy that you'd get from carbs or fat.
http://authoritynutrition.com/6-reasons ... a-calorie/ Protein has other important uses in the body and it's not always easy to get enough of it for those functions, so the body is programmed to use up the carbs and fat first. So if there are complaints to be made about birdseed, it's that the grains (like millet, canary grass seed and oats) are too high in carbs and the oil seeds (like sunflower and safflower) are too high in fat. These seeds don't provide enough complete protein anyway, so the body can't afford to squander it as an energy source when better sources are available.
Morning seems to be the time when calories are needed the most though. Nothing has been eaten for hours and the body needs to replenish its supply. When it comes to human weight loss, they tell you to eat more in the morning (because it helps jumpstart your metabolism) and eat less at night (because fewer calories are burned then and it's more likely to get turned into body fat). Birds slow down their metabolism at night just like humans do so it probably applies to them too.
Fatty liver disease is caused primarily by overeating and obesity. I know people who say it's really a malnutrition problem, because birds eat too much food in an effort to get the nutrients that their diet doesn't have enough of, which often includes a protein deficiency. For example the Merck Veterinary Manual at
http://www.merckvetmanual.com/mvm/manag ... cines.html says "Deficiencies of vitamin A, protein (the amino acids lysine and methionine, in particular), calcium, and other nutrients are seen in most psittacine species on seed-based diets". Tthe previous sentence specifies that they're talking about an all-seed diet.
Protein isn't considered to be a cause of obesity, and in humans at least there are those who say that high-protein diets help with weight loss and prevent obesity. I don't think the relationship between protein and obesity has been studied in birds, but I do know that some avian vets who are very knowledgeable about nutrition primarily blame excess carbs and fat for avian obesity. They even say to limit fruit because it's too high in carbs (simple sugars) compared to the amount of vitamins and minerals you get out of it.