+1^
I doubt it would actually blow up. But it will eventually fail. And cheap PSUs have a bad tendency of taking something else out with them. If you were sure you would never use the card at its max capacity, you may get away with it for awhile. Maxed out, the GTX 280 is a 236W card.
http://www.hwcompare.com/1463/geforce-gtx-280/
That will draw 19.7 amps on the +12V rail when maxed out. Does you 450W PSU even have a 6 pin and an 8 pin PCIe aux connector for that card?