Yes, you need to use a pretty large gauge (thickness) of wire, then you further harden it by tapping with a hammer.
Excellent question, though - the stiffness, or temper, of the metal is a very important factor in wire jewelry.
You can also begin with stiffer wire than "dead soft" - for example, "half hard" wire will be stiffer to begin with. The drawback is that it's harder to make loops than it is with softer wire.