Are you saying that you have tried to change your reservation and were not able to because the room you want isn't available? And you think if you call they can find a room? If that's the case, they can't. The availability they see is the same as you see.
Now, what you can do is make sure you are looking at all the options. For instance, if you booked a room under a promotion, when you go to check for availability for a different room it will still show rooms using that same promo, provided it's not expired. If it is showing just the promo rooms you may find other availability by switching to Rack rate, or even a different promo if there is one.
And it's REALLLLLLY unlikely you can change when you arrive. Availability is extremely tight. I would never count on it just because you've done it in the past.