Low long is serious for a cat that hasn't pooped?

I have a 14 year old cat that is currently going through a bit of a crisis healthwise. He's under a Vet's care and taking Clavamox for the past week for a bit of a liver problem. So far his appetite has been pretty shot and there's not been much eating or drinking like usual. There is some and it's enough to produce two small urine deposits in the litter box but to my growing alarm, there hasn't been any poops for a good week. Is it normal 'considering' the food intake is so drastically cut back? So far the antibiotics don't seem to be bringing him back like the Vet claimed. Plus to make matters worse, he has had for years this large tumor right smack in between his eyes, resting on the nose. (It would not be a good idea to have surgery to remove it as it would create a defect and he'd need a skin craft that may not heal being he's a cat that would mess with it, etc.) So there is some congestion as well that the Clavamox is failing to knock out. One Vet from a visit about a month ago theorized that the congestion could be from the tumor pressing in on the nasal cavities. Just when I think all hope is lost, my cat will show brief periods of lucid, 'normal' behavior so it really is keeping me in a state of hopefulness mixed with despair. My family is seriously considering putting him out of his misery if the meds fail to restore some quality to his life. We can't stand seeing him look so miserable.
Thanks in advance for your thoughts.