Keyesian Kool-Aid... Gov't spending begets greater tax revenues? If this was the case, why hasn't QE earned back enough to close the budget deficit or reduce the Federal debt (and/or debt to the Fed)?
Because it can't...
If you'll stop and think for a moment , you'll realize that your post is absurd, as it implies that during a recession, when the government is leveraging up by borrowing and injecting money into the economy, that, if those who claim federal spending increases revenues were right, the additional Federal revenues should "close" the budget gap. What makes this absurd is that you have totally disregarded time!
Of course increased government spending in the domestic economy, given a little time, does increase Federal
revenues. There has never been any question about that. At first, the increase in Federal revenues is only a small fraction of the additional money spent. Over time, however, the revenues returned to the Treasury, per each dollar injected into the economy typically increases as the injected money circulates in the economy at an accelerating velocity as recovery occurs. Meanwhile, assuming the injected money was borrowed, the Treasury will pay interest on the borrowed money. In good times, however, injecting money faster than justified by productivity and growth is harmful! The central bank may have to remove some of the money injected during a recession once good times return.
But regardless, Federal spending in the economy does, in general, increase Federal Revenues. And Federal spending is typically increased during recovery from recessions to compensate for reduced spending in the private sector and to spur demand and get the economy moving again.
No economy can grow forever without limit. The ideal inflation rate is exactly zero with absolute stability in the economy at full employment (5-6% unemployment). That is impossible to maintain, however, without incurring great risk of deflation. Therefore, the Fed sets an inflation target near 2%. Setting a higher target allows too much inflation, and setting a lower target risks deflation.
(Intentionally reducing revenue to increase revenue by lowering tax rates does not, sadly, increase revenues. Unfortunately, the result of reducing tax rates is just what any uninformed sixth grader might have guessed, i.e., a reduction in revenue. An uninteresting and disappointing result to be sure! As we later learned, all of the increased revenues during our trickle down experiment of the 1980s came from massively increased government spending, none came from lower tax rates. This was the great disappointment of the 1980s. Today, those trickle down ideas seem silly. Back then we theorized that both private and public sectors could become "richer" by moving money around in a way that would increase productivity in the private sector. To our dismay, the thing that did prove effective in increasing private sector productivity was to increase demand by spending more federal dollars! Just moving money around, by itself, did not increase productivity -- To save face, Dr. Laffer had to deny knowing anything about that infamous cocktail napkin that Dick Cheney remembered so clearly.)
A recent concern of the Fed has been the build-up of bank reserves. That is to say when the Fed recapitalized the banks during the recent crisis, much of that money sat idle in the bank's reserve accounts at the Federal Reserve and was not circulating. Obviously this idle money was not producing nearly as much Federal revenue nor private sector productivity as the Fed would have liked, so the Fed pursued various means, it has many arrows in its quiver, of getting banks to lend once again.
Obviously, there are recessions so deep that money injection alone, via lowered interest rates for example, is an ineffective cure. In good times, responsible governments only inject in proportion to growth in the economy. During recessions, they inject money to stem further retraction and to get money moving again by increasing demand. If the demand is not coming from the private sector then it must come from the government sector via government spending. If it turns out that too much money has been injected, and as a result inflation is heating up, money can be taken back out of the economy. The Fed has the tools for doing that as well.