Stipulate, arguendo, that government spending is stimulative.  In order to pay for the stimulative spending, government must collect taxes or borrow.  Taxes taken away from the citizens, though, is money the citizens no longer can spend.  Raising taxes to pay for increased stimulative spending is even more money that those citizens now cannot spend.  This reduced private spending offsets the public spending funded by that taxation.

Increased taxes to support increased public spending reduces private spending even more than the amount of the tax increase, though.  The increment above the simple reduction in private spending comes from individuals and businesses now being especially careful to husband their monies: they increase their savings so as to improve their ability to handle unforeseen problems, such as a medical emergency, a roof repair, a capital plant problem, another increase in their tax bill beyond the one just suffered.  Thus, private spending is reduced further by increased saving, and a tax increase results in a net reduction in the sum of private and public spending.

This offset doesn’t change when government borrowing, rather than tax increases, is used to fund stimulative (government) spending.  Americans aren’t stupid.  We all recognize that today’s government borrowing is just tomorrow’s increased taxes and/or rising inflation, and so the above husbanding still occurs.

This is a relatively symmetric relationship.  A reduction in tax rates achieves two positive things (although after a minimum threshold, the second positive becomes a wasteful negative).  The first positive thing is that more money is left in the hands of private individuals and private businesses.  This additional money is either spent, which is directly stimulative, or it is saved against one of those unforeseen events, or for a planned large expenditure, future retirement, or future investment.

Thus, saving is stimulative tomorrow, and more than that, the saved money actually serves two stimulative roles.  One role is that this is the money private individuals and our businesses are going to spend tomorrow for one of the reasons just described.  The other role is through private or commercial lending/borrowing.  Those savings are assets that banks and other financial institutions can lend to our neighboring private individuals and to our businesses, so our neighbors and businesses have increased money for their current spending.

The second positive thing is that with these reduced tax rates, economic growth is encouraged, and that increased economic activity generates more revenue for the government beyond the direct reduction from those reduced rates.  However, since government has no need of money beyond funding the few things our government was created to effect, any amount beyond that level is wasteful and so provides room for reducing tax rates even further.

Finally, in the real world, where (Keynesian) stimulus spending has been shown to be wrong empirically (vis., FDR’s “stimulus” spending during the Great Depression, which prolonged the Depression; and Obama’s “stimulus” spending in the present deep recession, which is prolonging the recession), reduced government spending also is net stimulative.  Government spending crowds out private spending through at least two mechanisms.  Government demand artificially elevates prices compared to the level at which those prices would exist in the face of solely private demand, and private spending is reduced by lack of need to purchase: the government will buy and transfer the goods to the private individuals.  Reduced government spending reduces that crowding out, and private individuals and businesses return to the market place.