Andrew, there is some empirical evidence that Speaker Boehner is right.
As is often the case, we can look to the American states for some guidance. It turns out that in 23 U.S. states, the government will automatically shut down in the event that the governor and the legislature fail to agree on a budget. In his work on budget rules, David Primo examined the theoretical impact of these provisions from a game theoretic perspective. He noted that in states with an automatic shutdown provision, “the legislature will be able to achieve its ideal budget, so long as the governor prefers it to no spending.” (p. 102)
He therefore predicted that states with such a provision will spend more than states without such a rule. He then tested the hypothesis, controlling for a number of other factors known to impact state spending and found that states with an automatic shutdown provision actually spend about $64 more per capita than other states. As he notes, “This effect is remarkably large, given that shutdowns occur rarely.” (p. 103)
This suggests that the federal government’s automatic shutdown provision—by making Congress’s desired spending level a take-it-or-leave-it offer—tends to bias the government toward more spending. By extension, it also suggests that a government shutdown will shift negotiating power toward those who favor more spending. So, paradoxically, fiscally-conservative Tea Partiers stand to lose the most if the federal government shuts down.
I’ll buy that this shows the legislature has leverage over the executive in “shutdown” states, but I’m not sure if I buy the “by extension . . .” bit in the bolded section, precisely because in power distributions like the one we currently have in Washington, the locus of the shutdown fight is within the legislature and not between the legislature and the executive. (President Obama has shown himself again and again to be uninterested in taking a leading role.) Under this dynamic, it’s easy to see the House Republicans as the ones with the leverage, and the Senate Democrats as the ones in the bind — since like the executive in the paradigmatic case above, they prefer some spending to no spending at all.