It generates jobs and helps boost the economy, which helps increase the tax base and keep more people off the welfare rolls. Every dollar spent has a 1.5 multiplier effect on the economy if I remember correctly.
In the long run, it's also much less expensive to invest in our infrastructure than to have to clean up the mess after it collapses. They say that an ounce of prevention is worth a pound of cure, after all.
The same argument holds for this truth as does in a regular household. If you constantly nickel and dime things instead of taking care of the big stuff, you will end up paying out more money in the long run. Our country's infrastructure has been let go for a very long time, mainly while financing wars. If our infrastructure had been built up, for example, in the New York downstate area, the effects of Hurricane Sandy would not be as exorbitantly expensive. Spending money on infrastructure is something our government needs to be strongly dedicated to.
As a Civil Engineer myself, I know first-hand about the degrading infrastructure in our country. Many of these structurally deficient bridges and other transportation systems need to be replaced now. Construction is only going to be more expensive in the future. Also, if we wait until these structures fail and collapse, it will cause mass casualties, not to mention a lot of extra money will have to be spent on the disaster. Finally, our economy is greatly dependent on infrastructure itself.
Infrastructure is incredibly important to how a country works. In order to work smoothly, the infrastructure needs to be in good condition and it needs to be effective. Improving these things would, in the long run, keep the government from having to spend so much on upkeep costs and, in turn, would free up more money to spend on other things to reduce debt.