The short answers IMHO are:
Impossible? No. On any day at any time, somewhere within the 47 square mile World, there is probably a TS restaurant (probably many more than one) that is ready to seat you right now or within the hour.
Difficult? A big maybe. It depends on what your definition of difficult is. It depends on any number of factors, mainly: what restaurant do you want to eat at (some are much more popular than others)? Are you willing and able to park-hop or travel to a resort to eat? Are you willing to take a reservation at an off-peak time, like 4:15 or 9:00 for dinner? The bottom line is that sit-down dining (what is called TS on these boards, for Table Service) is popular - more popular than ever, due in part to the
DDP.
Like most things at WDW, the farther in advance you can make your plans, the best chance you'll have of getting what you really want. This can be something as simple as checking at your hotel before you leave for the parks that day to see what's available in terms of ADRs that day, or even calling Disney Dining from your cellphone (or checking at Guest Services) a few hours in advance of when you want to eat. Your choices might be plentiful or few, but there will be choices, and then you can decide if any of them work and then plan accordingly. The least likely way to be successful is just walking into a place. You might be told the wait will be too long for your liking, or you might be told that they're booked solid, and you could spend the next half-hour walking to three more places to find the same situation at all of them. Or you might get lucky and get seated right away at the first place you check. Again, "it depends."
Good luck and have a great time!
