After you defeat Logan, the next few (eight or so) good choices leave you with no money in the treasury for the coming war. Can you still win? I'd hate to invest a lot of time and still lose.
Yes, you can still win the game if you go into the final choice with $0 in the treasury and by making all good decisions.
The amount of money you have in the treasury before your final choices only relates to how many people survive the war. You can transfer any money earned personally from your account to the treasury as well before making your final decisions.
You can make all good decisions and still have enough money in the treasury for everyone to survive the war ... in addition to simply waiting for real-life time to pass, as Raven mentions, you can do other quests in between your assigned tasks. There is nothing that says that you must proceed directly from task 1 to task N and then war.
The best time to do "other stuff" is before the last task on a given day. Once you complete that task, the game will advance to the next day. (I think there are one or two places within a day where one task immediately follows another, but I haven't finished it recently and can't be sure.)
Regardless of how you get money from other quests, as in Blake's answer, you can transfer some of your personal money to the treasury if needed. The key is to spend enough time doing other things to build up enough total money to make good decisions and lose no citizens, if that is what you want to do.