Wow, I can relate.
If your cat survives this immediate insult (illness), will he be continent (able to control his urine)? Speaking from experience, an incontinent house cat is just about as bad as it gets.
I would ask the vet frankly about the bill, since a retained catheter started the complications. I'd be agreeable to paying for the intial procedure and meds, but the complication repair and extended hospital time should be his responsibility.
I know the worry of "how can I put a dollar value on my dear pet?" There is no clearcut answer. Do you have a family that loves him, too? Is money very tight at home? Would paying the vet for continued care seriously affect your household budget?
I paid $750 for my old calico cat to have her ear canal reshaped, as it was chronicly infected. Although she survived and recovered, the suffering she went through convinced me that I would never do that to her again. Now she has cancer, but is eating okay, purring, and more vocal and interactive than ever. The DAY she is visibly uncomfortable I will have her put down. She is my 18 year old handicapped pal.
So do whatever you think best, and don't forget to pray to thank God for giving us the joy of companion animals--and their example of unconditional love.