The answer I think is that most conservatives don't actually believe in it, they just pretend to. It lingers for a variety of reasons. Partly I think it is because there is a lot of hatred in this country. For whatever reason a lot of people like the idea of severing people from the perceived welfare state (even themselves in some cases) and this gives them an excuse.
The bigger issue is that theoretically there actually is a grain of truth in the idea. Creating a more favorable business climate SHOULD lead to higher employment and spur economic growth. It doesn't happen automatically though, and the original supply-side economists understood the theory as a targeted and strategic policy choice, not a system-wide initiative. The original supply-side economists were more like surgeons cutting off dead patches of skin knowing it would grow back and improve the overall health of the body. The modern-day caricature of the theory, however, is a hatchet-man, lopping off entire limbs.
Conservatives use this grain of truth as justification, but in reality, I think most are just doing the bidding of their corporate masters, who simply want the reduced regulations and taxes that will let them make more money. How the Republican party still has any adherents after the Bush cataclysm is baffling. It's not like their policies are much different. If anything, they are even further down the rabbit-hole. There certainly isn't any mystery to them or what will happen if they are elected.