You don't need a big budget at all. Let's compare to X2, which had good effects and a $110mil budget.
-"Wolverine" needs to pay 1 x-man, not the whole ensemble cast (atleast not Halle, so that saves a ton right there)
-The only special effects really needed are the claws and healing factor: no explosions, no weather changes, steeling or icing up, etc.
-"Wolverine" is being treated with respect in terms of time, unlike X1 and X3 (whose budget was ridiculous because of time). They can take their time, hire less SFX companies, not rush editing, etc. In terms of scope, I still felt X2 had a rushed schedule- they began shooting mid-summer a year before release, and there were a lot of effects and editing to be done. From what Hugh has said, they're starting serious production this fall/winter, so it definitely won't be rushed (plus they writer has been working on it for a while now).
This movie, if done right, will be a low budget, and to please FOX definitely bring in the cash (although I'd rather have an X4 than any spinoff). It should be a good example of quantity not being reflective of quality.