Hi Amber! As a procrastinator, I'm often scrambling for last minute dining reservations at Walt Disney World myself, and I'm happy to tell you that if you're persistent, you can usually book the restaurants you want.
I'm not sure how large of a party you have, but I actually just checked and do see some character dinners available at various restaurants in two weeks. Head to the main
Disney Dining Reservations web page, insert your date and party size in the search boxes, and then search for "Dinner" rather than a specific meal time to pull up a list of all restaurants with availability for that evening. You can check the Character Dining box to filter the results. I've found that this broad search method gives you better results than searching a particular restaurant for a particular time. However, if you have your heart set on a certain restaurant, such as Chef Mickey's, then keep checking each day for openings, even after you arrive at Walt Disney World. I've generally found that guests cancel reservations in the days leading up to their vacations so it's likely you'll find an opening before you leave if you keep checking. If you aren't able to snag your desired character dinner reservation, call the Dining line from your resort room the night before and you'll often find availability.
Don't forget that you can also dine with the characters at breakfast and lunch, so if dinner is booked up at your desired restaurant, consider other meal times. Finally, there's always the possibility of obtaining a table by walking up to the restaurant. Your best bet is to check for availability at the beginning of the dinner seating or later in the evening, rather than at the peak meal time.
Wishing you a magical vacation with lots of character meals! Come visit us again at the Moms Panel if you have more questions! We'd love to help!