Keynsianism is a quite simple missconception.
The essential point is, that it distinguishes between consumption and investment. The true point hereto is, that business cycles are never caused by consumption behavior, but always by investment. It is sinkind investment causing recessions, and rising investment causing economic booms.
However, whether you purchase a car in order to use it as a cab (=investment), or to drive if just for private use (=consumption), obviously does not make any difference for the car seller. Either way he gets the money that you spend, has additional income so to say. As the multiplier model suggests, that only the propensity to consume will keep the money moving, while the money that you save will not, Keynes obviously has a problem with the equation saving = investment.
Keynes thought is, though it is never told that explicitly, that during recession savings do not make to investment. This is sound idea! In fact it comes very close to the nature of recessions.
Just image such a scenario. People are still saving a decent part of what they have, but hardly anyone would like to invest as long as the prospects look gloomy. So what happens? There is a lot capital not moving anywhere. This is basically a traffic jam on the capital market. Money is moving in, but not moving out. The velocity on money is declining, which has very much the same effect as a reduction in monetary supply.
Now what if the government runs into debt? All the capital not happy with risky and unattraktive investments in the private sector, could now be invested into relatively safe government bonds. The traffic jam could be slowly disolved.
Alternative ways would be lowering interest rates, thus making look private investments more attractive. Or to raise monetary supply, to replace the money stuck in the jam.
So what is wrong about Keynsianism? First off all, it is always explained the wrong way. Its skope can not be to spend more, it is rather about publishing government bonds and thereby helping out investors.
Secondly, there is no additional money just because the government spends more. The government only spends money that it takes from private investors.
Thirdly, the “multiplier” does not work the way it is generally told. There is no difference between consumption and investment with regard to the money continuing to circulate, so that we would need to add the propensity to invest to the propensity to consume. We could thus calculate the muliplier by m = 1 / ( 1 - c - i ), which would result in 1 / 0 = indefinite!!
Fourth: this example shows quite well the basic missunderstanding. An indefinite multiplier is true, in the long run, for additional monetary supply (including the negative side effects). That is the origin of the Keynsian multiplier. He simply confused it with the effects of monetarism.
Fifth: the only scenario, where deficit spending could actually help, is a situation where the capital market is stuck in the way described above. But even then, the “traffic jam” is self healing, in the way that the additional, uninvested savings will soon rush into new investment opportunities and thus counter the recession with additional growth. This will not happen if the capital has been “nationalised” in the meanwhile.
Such extreme blockades in the capital market are rare. The banking crisis or the great depression are the only examples I could think of. Both were caused by ill fated monetary policies. All the rest of deficit spending, and Austria for instance did not have a budget surplus through the last 40(!) years, is just running into debt.