Right now I am at work so I would have to go home first. Boss couldn't stand to pay us for two whole days without working so have to work a partial day today - but he is the boss so what can you do . Have multitudes of 5 gal buckets in the garage that would do until could get an outhouse done in the backyard. Improvise a seat with some kind of cushioning or cut a hole in one of the lids. Don't have much on hand in the way of freshening, maybe some baking soda or a shovel of dirt, might get lucky and have some kitty litter on hand. Most likely dig a hole in the yard and empty it as we go, cover it with a garbage bag and leave it in the garage, or dump it into the storage tank. The last one made me think there might be a longer term strategy of just building the outhouse directly over top of the storage tank. Hmmm. Since no flushing = no water I would want to have a good supply of hand sanitizer on hand as well.
Not trying to criticize or hi-jack as these are great scenarios to think about. However I am, admittedly, probably more like the rest of the population than others on this forum (I am working on that). Unless I had advance warning that services would be disrupted for an extended length of time I would probably be like most people and continue to use the toilet for a few days hoping I could eventually flush it. I do have an advantage of water not being an issue when power goes out (at least as long as the storage tanks hold out) so we can still flush when tank #2 is emptied (don't bother flushing in this situation for tank #1 - before anyone asks this is my eight year olds and my current explanation for pee - empty tank #1 - and poo - empty tank #2). If it became obvious this was going to be an extended outage situation then I would go to plan B (buckets and outhouse if necessary). We also are fortunate to have additional water sources VERY close by - a small stream running along one edge of the property that empties into a small river running along the backside of the property, and not nearly as far away as it sounds (less than 100 feet at the farthest point and much closer at others) so drawing water for a flush, while inconvenient, wouldn't be a problem (see comments below for possible problems with septic system though). Not sure I would want to drink any of it. We could filter it and boil it but there could be other chemical nasties that would still be there. Point being in a situation like this drinking water would likely be more of a concern than the ability to flush. Again not trying to hi-jack, just thought I would mention that. Everyone else behave yourself and stick to the original premise of the thread.
On the need for electricity, there is another concern other than what has already been mentioned. Ours is a small aerator sytem so electricity is required for the little motor that spins an agitator that aerates the storage tank - I think it also starts breaking down solids and prevents them from sinking to the bottom. Not sure how long we could go without it. I believe the rest of the system is basically one tank fills and overflows into the next, eventually leading to a sand filter that is basically a type of leech bed and any excess goes through a chlorinator and then empties into the river I mentioned earlier.
Oh and live in a house with a yard outside city limits.