You still can make it if you (Quickly) find a US Post Office near you that can expedite your paperwork. The post office now has special locations that will handle all aspects of passport renewal (Photo's, application etc.) So it makes it easier, It cost a bit more (to expedite passport) but I got mine back within a couple of weeks. Belize Immigration
most likely will not let you in the country if your passport is within 6 months of expiration. Good Luck, It is still possable if you hurry up