Kuki, I thought Homeland Security required 72 hours before sailing?
NancyB, as long as you can find a ship with cabin's available you can book up until either 24 or 72 hours

.
Generally, the last minute availability will be inside cabins. As long as that's not a problem, go for it! Oh, yeah, if you're flying to the port the airfare will probably be higher last minute. Driving from AR to Galveston would probably be your best bet to keep cost's down.
I agree with Kuki, the best prices are
usually right after final payment is due.