Could government spending be profitable?

Economists speak of the multiplier effect of government actions in regard to taxes or spending. Recently I heard two claims on this, that a dollar spent circulates to a dollar and sixty cents of economic activity while a dollar of tax cuts circulates to a mere thirty cents. I doubt these are numbers that anyone will agree on, but there were two parts that stood out: first, that spending did a lot more than cutting taxes, second, that a dollar of spending creates more than a dollar of activity.

The second one made me think back to the cycling of money and what stops the cycle: taxes. By that I mean that the dollar is spent, some taxes taken out, the remainder spent, some taxes taken out, and so on. Eventually it will be whittled down to nothing, having returned entirely as taxes. This would seem to make spending neutral, as in theory it will always trigger that amount in increased taxes from economic activity. But there's another way for the money to stop moving: saving. At some point the entire dollar will be taxed or saved and it is the saving which prevents it from cycling fully around to balance the budget.

This suggests that the ideal way to stimulate an economy is to tax savings and then spend the revenues from those taxes.

On the profitable side, the newly flowing dollar and the resulting demand would encourage saved money to be invested, putting it into he flow as well, where it is taxed, and now the dollar of spending has freed up more than a dollar of incoming taxes. Profit! Also known as a surplus, the strangely forgotten opposite side of Keynesian economics.