From Economics One blog, "Stimulus Math: Many Multiples of Nothing is Still Nothing" by Stanford economics professor John B. Taylor:
States used stimulus funds to replace their borrowings. Government spending did not increase. How could there be any stimulus effect from these federal funds to states and municipalities if spending at the local level did not increase?
Economic research, from as far back as 1979 by Ned Gramlich, showed that federal stimulus funds substitute for state and local funds with little if any increase in spending.
See John Coogan and John B. Taylor's excellent article on this topic in today's Wall Street Journal, "The Obama Stimulus Impact? Zero: Liberals are still arguing that the federal spending stimulus wasn't large enough. How many multiples of nothing—its result according to new evidence—would they like?"