The first problem is treating accounting identities as causal mechanisms, as in "elevated excess private saving (firms and households) keeps the government deficit in the red." People, you can't do meaningful comparative statics on accounting identities! There is no causal chain in an accounting identity!
The second problem is that Wilder is making up variables on her own account namely private excess savings and corporate excess savings. She is somehow able to divine these clearly endogenous and unobservable variables from the Fed's flow of funds data (I believe by assuming that ALL saving is excess saving*)! Personally, I would say that by definition, from the point of view of the household, excess saving is always zero!
The third and most egregious problem is conflating correlation with causality. Wilder shows that the correlation between the "corporate savings glut" and unemployment is .71 and leaps to the conclusion that corporate savings is causing unemployment! Of course it is equally possible (given the analysis done there) that unemployment is causing corporate savings.
But the most likely situation is that some set of third factors are causing both unemployment and corporate saving. Both of these variables are clearly endogenous in any sort of general macro model, and a realistic analysis would need to be with something like a structural VAR based on a clear identification scheme.
Corporate cash balances are high. Unemployment is high. That doesn't mean that one is causing the other.
*here is Wilder's stated definition: The excess corporate saving rate is the residual of the Current Account (external saving) net of government and household excess saving.
I didn't see a definition of household "excess" saving.