So sorry to hear about Jasper! Crossing my fingers that it isn't permanent, but in the meantime a second opinion sounds like a good idea.... I personally wouldn't make the drastic decision to euthanize based on one opinion from a vet I didn't already have a good relationship with. Also, even if Jasper remains paralyzed, there may be options to keep him happy and comfortable. There's a great website that helps people deal with situations just like yours:
http://www.handicappedpets.com/
Good luck!