David, Welcome to LJ’s. I’m sure you’ve already figured out from the advice so far that trying to do a bandsaw box with a jig saw probably wouldn’t work.
I’m with AaronK and Tomoose, maybe you could find a cheap used bandsaw on Craig’s list or see if there is a fellow LJer in the area that might let you use their bandsaw to make a box. You’re more then welcome to use mine, but I think Myrtle Beach, SC might be a little far. LOL.
Bandsaw boxes are a lot of fun to make and they make great gifts, so be prepared. Once you do one, you’ll want that bandsaw so you can do another….........the only limitation to making a band saw box is your imagination…...and the size of your band saw!. Good Luck.
-- John @ http://www.thehuffordfurnituregroup.com