Hi there, Jennifer!
As you are aware, Disney on New Years Eve attracts loads of visitors from all over the world. And yes, everyone wants to share the magic on that special night.
It is likely that at some time during the day, one or all of the Parks will reach capacity and will need, by order of the Fire Marshal, to be closed to any more visitors.
As a Disney Resort Guest, you are promised entrance into
a Park, but it may not be the Park of your choice. And if the Parks are full, obviously you will not be permitted to enter. This is a safety issue, and Walt Disney World is primarily concerned with the health and welfare of its Guests.
That said, you might need to decide if the risk of losing your "spot" at a Park is worth the reward of Chef Mickey's (my favorite restaurant, to be honest!). Do remember that Disney offers loads of other non-Park options for fun on that special night if you choose to keep the dining reservation.
Feel free to contact me if you'd like some non-Park ideas for ringing in the New Year, Disney-style!
See you later, celebrator,
-Deborah B.