To some extent he can be criticized for acting in his own interests, rather than his state's. The money, after all, is already appropriated; his protest of refusing it accomplishes nothing for the state, though it does, modestly, help the federal government's finances.
Haley Barbour, however, has explained that a great deal of the stimulus money is not "free." (Of course it's not free, but I mean it's also not free of strings.) A lot of the stimulus comes with unfunded mandates to change state law -- for example, some money comes with the string that the states will have to offer unemployment benefits to part-time workers who lose their part-time jobs, which many states (if not most) have never done.
In classic Chicago fashion, it's pay-for-play.
So partly, Jindal can make his case that the "aid' actually hurts the state to some extent; I hope he does make this case, because I wouldn't want to see him punished at home. He can make the case for federal policy eloquently, but he must make sure his constituents do not resent him for acting as a federal official rather than a state executive.
He Did Make That Case: As several commenters tell me, he laid out that case on Meet the Press. Video below.