Paul Krugman notes that there's a simple relation between the 'private sector surplus' and the interest rate. He uses graph above to show that the higher the interest rate, the more the private sector--consumers plus the businesses they own--will save.
Fine enough, that's all partial equilibrium analysis. That is, the capital goes outside this system, and the price of riskless capital (interest rate) is set exogenously. Supposedly:
in normal times the central bank can reduce interest rates enough to set this surplus at zero, or no larger than the public sector deficit, thus ensuring full employment
In stressed times after a bubble (eg, the 'after' line above), the private sector tries to run a big surplus as it pays down debt. This causes recessions, which can be mitigated if not eliminated via countercyclical budget deficits by the public sector.
This argument would be tenable if it were 1936 and people never tried it, but it has been tried over and over and if a government could spend itself to prosperity and stability, a couple such countries would demonstrate this. Instead, we have the examples of the contrary, where fiscal restraint and modest automatic stabilizers were consistent with the wealthier countries post WW-II.
But what I love is the way Krugman totally ignores the heterogeneity of investment and employment, and simply thinks that people and companies are saving 'too much', and so anti-savings by the government would offset this, leading to full-employment bliss. That kind of thinking is profoundly misleading.