There are TWO types of "days" in the game
1) "days" as in the game going from 00:00 back to 00:00. When that happens you pay your family upkeep. I think this is 15-20mins.
2) "days" when you are a king. Those "days" will NEVER advance until you finish your "daily decisions" So if you have 339 days till the attack, you can keep it there, FOREVER, and keep doing side quests, MP, etc until you go into the throne room, make the decisions, then usually do the "quest" that will "end" that "day" or time period.
Where you really need to be careful is when it says 121 (i think) days to the attack. It will JUMP from there to 1 (which is really 0). So don't do ANY kingly duties when it's day 1xx till the attack unltil you are 100% ready.
On another quick note:
People running around, FREAKING that they lack money.. or became king with low money.. DO NOT NEED TO WORRY... just hold off the story line AS LONG AS YOU LIKE.. earn enough $$ to make the decisions you want to make as king.. THEN move the story forward
If you are out of quests (and don't have anything else to do in game), you can simply just repair all houses and business and leave your Xbox on and idle for like 7 hours while you work/sleep/school. Even with rent at LOW on everything... as long as you own everything ownable.. you will rake in about 70,000 every 5mins... or 840K/hr. If rent is normal on everything, that ammount is doubled... and you make about... 1.7M/hr. Don't worry if your xbox "pauses".. the game's internal timer NEVER pauses... so you can sit in the sanc or the internal menu and once you leave, you will instantly get all the money you would have normally gotten while playing about. This trick works WONDERS for people who have to go to work/school. Just remember, most houses go from 100% to 0% in about 10 hours. Also make sure, if you do this, to tell the xbox itself not to turn off after 6 hrs of inactivity
Bowerstone industrial houses seem to drop faster... Also I noticed that the higer rent you charge, the faster the houses need repairing (not sure why they do that)