Multiplier

Can someone explain to me how the concept of a multiplier (>1) makes any sense at all?  Not whether there is one...I'm not that interested in that right now...but whether the concept makes sense under basic econ theory?

My understanding:
If the government taxes, then money that a private individual had is now had by the government. 

The private individual would have given X% to someone else (spent it), who would in turn have spent Y% of it, and so on. The rest would be saved, and thus invested by the saving institution (assume a lending bank). 

Instead, the government gives it to someone else, who still spends Y%.  Are we suggesting that the value (1-X%) towards spending instead of saving (for loans) results in a massive difference?  Are we suggesting that the government with it's Fatal Conceit knows where to spend (and even less likely, will follow the knowledge, rather than lobbying) that money better than the private individual? 

My understanding was that in general, we have nearly 100% empirical evidence that for almost all problems, centralized governments do not know where to put $ as well as individuals.  It seems insane that someone could claim a 3x multiplier by doing anything other than ignoring Bastiat.

So...if taxing doesn't work...then let's borrow.

Now that we have a robust futures market...and good future-looking predictions...doesn't borrowing money now, to spend later have the same result?  It simply creates a future obligation...which results in a net future prediction of having to save more to pay taxes...which is taking money out of the private economy?

Someone educate me.  I'm not real clear here.