Perhaps Krugman is drawing from Barro's 1981 JPE paper on government purchases, which does indeed derive the stated result, but that is no longer the dominant approach. Circa 1990, Aiyagari, Christiano, and Eichenbaum note:
On pp.4-5 they explain why Barro is incomplete.
Overall I find these debates confusing. I wonder for instance if Krugman's blog example is actually comparing tax finance to debt finance, rather than temporary vs. permanent spending shocks. (Note also that Krugman is making a claim about demand or effective "stimulus" rather than output and employment, although I am taking the latter as what matter.)
Those of you with lots of time on your hands can ponder whether the "permanent vs. temporary" debates compare "$100 billion this year vs. $100 billion for each year to come" and/or "$100 billion this year vs. the present value of $100 billion spread out over time, in perpetuity," and whether all cited articles and blog posts are making exactly the same comparisons.
Results in this area usually can be modified by further assumptions. I think of this as the central paper, published in the JME 1999. Admittedly it is for a small open economy but the key result is:
Moreover, permanent increases in government expenditures have larger
positive labor supply and output effects than temporary fiscal policies.
Again, I don't have faith in these models and I believe agnosticism is the correct stance. The point is not about who is wrong and who is right but rather how treacherous these analytical waters can be. Beware!
In any case there is hardly an overwhelming brief in favor of the stimulative powers of the temporary spending increase. The best case for the temporary boost is I think the public choice argument that it is better to get it over with more quickly, so as to limit corruption of the government.
Addendum: Megan McArdle adds comments on her contribution to the debate.
Second addendum: You'll find a response from Paul Krugman here. I'll note it is he that introduced the framework of Milton Friedman and the permanent income hypothesis, not I. If you look at the literature as a whole, it can go either way whether the permanent or temporary increase in government spending is more potent. Krugman's own example doesn't demonstrate his point that the temporary increase is stronger, as it compared debt-based to tax-based finance rather than permanent vs. temporary.