B767 Captain reported refusing an aircraft due to inoperative lavatories despite pressure from company maintenance to accept the aircraft and defer the lavatories for an 8 hour flight.

Narrative

We were scheduled to operate Aircraft X on Date from ZZZ to ZZZZ. We met up in operations and conducted our preflight tasks. Aircraft and weather were acceptable so we proceeded to aircraft. Got loaded up and pushed away from gate X. After engine start; the #2 generator dropped offline. We reset the generator control breaker and it was fine. We accessed the electrical page to monitor the volts and frequencies. All seemed to be okay as far as we could tell except in bottom left corner there was a message 'IDG OUT TEMP'. We decided to contact local Maintenance to see if that was acceptable and to see if there was any previous history. Local Maintenance deferred to Maintenance Control. After conferring with Maintenance Control; they advised us to return to the gate for maintenance to follow up. Maintenance worked on issue for several hours and finally was able to resolve the issue. In the meantime; the Purser informed me that there were 4 lavatories that had stopped working and had backed up/clogged. Lead Mechanic was very eager to get this flight out and advised me that everything would work normally once above 16;000 ft. due to pressure differential. We had a full complement of passenger and scheduled for an 8-hour flight. Plus; we were on the ground with folks on board for past couple hours. I reiterated my concern that I wanted these bathrooms work prior to departure. Maintenance confirmed large amount of paper towels stuck in the various bathrooms but reluctant to do anything about it. Eventually went downstairs and informed us that the blower/vacuum breaker had tripped and therefore we had lost the ability to flush below 16;000 ft... hence on ground. We were trying to see if there was a way to make this work but there were so many uncertainties as to this really working because paper towel was confirmed to have clogged the bathrooms. He eventually conferenced call us with Maintenance Control to explain how the differential pressure would work. I explained that while all that was textbook... there was no guarantee that it would work because there were tons of paper stuck in conduit. Line maintenance refused to cycle breaker to see if we could regain access to lavatory vacuum system not did anything to help unclog toilets. He kept saying that it was a big amperage breaker and by resetting if could do more harm. I beg to differ because we have 40 and 50 amp breaker in cockpit that sometimes need resetting. In any event that was their choice. Flight attendants were also concerned that these clogged lavatories could make things worse by allowing sewer water to run down the aisles present an unsanitary situation for an 8-hour flight. We found this to be unacceptable and insisted we get these lavatories working. Maintenance decide that they were going to defer these lavatories. Once I became aware of there doing; I contacted Dispatch and informed him of our situation. Dispatch said that the Operations Manager wanted to join the call. From the tone of the conversation; I could tell that he wasn't there to render assistance but rather apply pressure to accept this aircraft and get it to ZZZZ. He sounded like a parrot and basically repeated what he had learned from Maintenance Control; how the system would work about 16;000 ft. I couldn't believe my ears as to why I am having a conversation with him. The only people that are responsible for the safe operation of this flight are the Pilots and Dispatchers. No one else should try to influence the decision making or to intimidate; by their position; or coerce into accepting an aircraft disregarding safety. Since he was on the phone; I proceeded to tell him into detail all that was happening. I believe I painted a pretty good picture. Eventually he let us know that there was another aircraft available but was being worked at the hangar and wanted to know if we would consider extending our duty day. I told him that I would discuss it with my crew and advise the Dispatcher. Unfortunately; we were not able to extend and flight was eventually cancelled. Something that we had discussed was the fact that if we had acceptable this aircraft with vacuum system deferred and eventually diverted; we would have a massive crisis on our hands. No lavatories and lots of fluids running down the aisles. This is not how I wanted this event to take place but no one wanted to do their job and were placing all the blame and pressures on the crew.