The theory behind stimulus spending is that when private spending and investment fall short of expectations, government can step in and make up the difference. Things like temporary payroll tax cuts, extending unemployment benefits, and grants for states to keep teachers in schools are great examples of ways the federal government can assist individuals, businesses, and cities, but they differ from infrastructure spending in a key way: while most stimulus measures are only needed as a response to recessions and shortfalls in consumer demand, investing in infrastructure and maintenance is something we need to do--but haven't--in booms as well as busts. What they share, however, is that recessions (and their recoveries) are always the best time to make these expenditures.
Why is this the best time to spend on infrastructure? Contracting is very cheap right now since construction companies are so desperate for business. Borrowing costs for the federal government are so low that investors are willing to accept a year-over-year loss on their bond purchases, after inflation (which is also exceedingly low). Unlike during a boom, we can be confident that public expenditures won't be crowding out private investment. And, of course, more people will have construction jobs, which lowers the unemployment rate directly as well as indirectly when those newly-employed workers start spending their money in the broader economy.
But for those who choose to believe that "stimulus" is just code for big government, socialism, etc., or that it doesn't actually boost the economy, infrastructure--particularly maintenance--is still a sensible way to spend our money. As has been widely reported, including on this blog, the U.S. has an estimated $2.2 trillion infrastructure backlog. Whether we choose to spend that money now or later, it's going to be spent. The longer we wait the worse the degradation and the more expensive each of those repairs will be, and the more it will cost us in vehicle wear-and-tear, lost productivity, and injuries and lost lives as pipes burst and bridges crumble. If we've got to make the investment either way, let's do it now, while the costs are least and the benefits greatest.