Reservations can be made up to 180 days in advance. They fill up from that date.
If you can't get a time you want, you can do a walk up.
What an ADR actually is, is a spot in the "reservation queue". So, ADR's get served first. Walk ups go in the other queue. Which does get served, but at a slower rate which is unrelated to how long the queue has become.
So if you show up with an ADR you're usually looking at about 10-20 minute wait for a table. As a walkup, if you're in a very off time like 3:00 or something, you can get in 25-45 minutes, or faster if the ADR queue exhausted. However, if you're hoping to walk up during peak times (because you couldn't get a reservation at peak times as per your post) the walkup queue is going to be long, and the ADR queue will be running full capacity, and Mouse only knows how long you will wait. At least they give you a pager and you can go a short distance from the restaurant while you wait, but you'll basically shoot an hour or two of your day, plus dine time (1hr), just to eat.
Counter service anyone?
One thing, if you ask at the front how long the walkup queue is, they'll tell you, and they're usually pretty accurate with their guesses in my experience.
The previously given advice to keep trying your reservation is good advice. Spots open up.
NB my time are from visits during slower times of year... might be worse in peak times...