My name is***** have been a veterinarian for 11 years. I hope I can help you today. I am sorry to hear that your pug is not feeling well.
Dogs that are still active and behaving normally, can go 3-5 days without eating and be fine (not the same for cats that need to eat every day). If he is stops acting normally/playful, then that is a sign that he should be seen sooner rather than later.
Dogs do need to drink every day though. So, not drinking for more than 24 hours is a sign that he needs to be seen.
Some additional things to look for to determine if he needs to be seen right away include:
1. If he will allow you take his temperature, then do so. Normal temperature is 100-102.5F for dogs. Elevated temperatures and not eating/drinking is an indicator to be seen.
2. Lift his lip to look at his gums (the tissue above his teeth). You want to look for a non-pigmented area (usually pink), if this area is pink that is good. You may press gently to make the pink area go white and then remove pressure and count the amount of time it takes for the area to go pink again. It should be 1-3 seconds. If it is prolonged or if the area is white (without pressing on it),brick red, blue, grey, or purple, then he should be seen (immediately if the color is not one of the "bad" colors that I mentioned).
3. Evaluate if his abdomen appears distended. If he is distended in the abdomen, and that is unusual for him, or if he gags or acts like he is trying to vomit without producing anything, then that is a sign of a potential problem.
4. If he starts to have vomiting or diarrhea, then he should be seen sooner.
Ways to encourage eating and drinking, include adding some low sodium and low fat chicken broth (warmed up) or the water from canned chicken or tuna to the food and/or water. You do have to make sure that he sees you do it though, that is part of them wanting to get to it. You can also offer a bland diet (2-3 parts cooked rice with 1 part boiled hamburger or boiled chicken). Warm up any food as well to make it extra stinky as the smell often stimulates appetite.
Please let me know if you have any additional questions. I am happy to answer them. If I have answered your question completely, please take a moment to rate me so that I may continue providing and improving my services. When you have a moment, I would also appreciate an update as to how he is doing.