"Not always. I mean, isn't this the reasoning behind the first dot-com bubble? At some point you have to turn a (operational) profit, and the more money you invest, the more profit you have to turn in order to recoup your investment."
Yes. Very true. Amazon is one of the few survivors of the dotcom bubble. For every Amazon there's a Boo, Pets.com, Webvan.
My response would be: those companies failed because they grossly overestimated the size of their markets, or were too early, or there was no market at all. If you overspend, you risk being the next Boo.com -- but if you underspend, you risk being the next Books.com. It really is all dependent on the market you find yourself in.
BTW, I am not personally attracted to "get big fast" cash-furnace type companies. The startup ideas I'm considering tend to be those in non-winner-take-all markets (ie, lots of small competitors, no one big competitor) where it's possible to turn a profit quickly.