How can you safely fix a crack in the side of the plastic base of a bird cage until you can get a new cage?

I would remove the bird from the cage during the repair if possible, then place Krazy Glue or another good adhesive glue in the crack, the put Duct Tape over the top of the crack to help seal it in place. The fumes from the adhesive may irritate the bird, which is why you may want to relocate the bird until the glue sets (about 10 minutes or so).