The graph at John Taylor's blog explains stimulus failure. (I wrote about the Cogan-Taylor work earlier, but it bears repeating.)
Everyone, including Keynesians, agrees that if Ricardian equivalence holds, then stimulus does not work. Ricardian equivalence means that the folks receiving the funds that the government borrows use the funds to save rather than to spend.
The Taylor-Cogan story is that in the case of the 2009 stimulus, a lot of the funds went to state and local governments, which promptly saved them (or, equivalently, reduced borrowing). The stimulus was not an increase in spending. Instead, it was a transfer between bank accounts. In other words, there was no stimulus. All the econometric modelers that applied their multipliers to estimate the effects of the stimulus are making bogus claims, because there was nothing to multiply.
If Taylor and Cogan are right (and I have not checked their work), then CBO, Blinder-Zandi, et al, ought to climb down from their claims that the stimulus saved umpty-ump jobs. That might be embarrassing for them, but it would show a willingness to be grounded in reality,