To answer your question .. it all depends on how busy the parks will be on certain days.
Most of the "big" rides fast pass availability initially "fill up" well in advance of the actual day. BUT, openings will show up occasionally if you look every day as people cancel their fast pass.
Just as an example .. since I have an active ticket (10-day no expiration) I can make Fast Passes whenever I want in the next 30 days.
30 days from today (10/15) .. Anna & Elsa, Seven Dwarves, Festival of Fantasy Parade and Enchanted Tales with Belle ALL don't have any Fast Passes left for that day.
Toy Story and Soaring still do.
This makes me think of a question though.
How does a site like the DIBB know the fast pass availability PER DAY for these major attractions.
And why doesn't Disney do that with their system when you are making your Fast Pass reservations?
Instead of picking a DAY and picking 3 attractions, why doesn't the system let you pick an attraction and it will show you what days FAST PASS is available for that attraction during the days of your stay? I would think some people would rather pick the day they go to a certain park based on availability of Fast Passes as opposed to picking the day first.