I vote for some type of fixed schedule, adjusted weekly is fine. I think there are two issues here, and one is being overlooked. Yes, the availability of the President and other cabinet members is important, and the amount of notice given may affect attendance. But the second reason for giving notice is so that decisions and polls can be posted in time! We have several issues ongoing (such as FP construction) as well as past examples (Leader, rushing, etc) which generated much debate in polls, but if we don't know when the next turn is going to be, it is hard to set deadlines for the poll!
For example, when we posted the polls about pop-rushing, I set them for 48 hours, since that was to be the next turn chat. What if (on only 10 hours notice), the chat was moved up one day? Can you imagine the outcry if citizens, who may have been at work that day, came home to find that we had already moved forward with those decisions. On the other hand, if it had been delayed another day, maybe more opposition would have built up, after the supporters had assumed the poll was already closed.
For this reason, I think a scheduled chat time is important, so we (cabinet members) can set our discussions/polls with a specific end date and a known time for execution. Also, our new turn instruction threads are based on the date of the next turn chat. If it is going to be 3 days till the next turn chat, I know how much time I have to work on something before posting my instructions. Since I don't have internet at work, it is entirely possible that notice could be posted, say at 1200 GMT (on GF's lunch break, or whatever), and I would get home from work at 6:00 CST (2400 GMT) to find out the turn is already underway, with no time to post polls, etc. (BTW, that is why I try to check the forum on my lunch break!).
If we know in advance that there will be a turn Wednesday, I can set polls up on Monday, and tell the people (those who vote, anyway) that it will end at 2300 GMT Wednesday, and that is when the decision will be implemented. We have polls that have run for a week, and no one knows when they will end, or even when they will be acted upon. The FP poll is a good example. It has been running, who is to say that during the last chat, the cabinet could not have started construction based on the highest total at that time, while many others didn't think it was done yet. With a schedule, a poll could have an end date AND an action date.