The robots can certainly be remade. House can purchase supplies from the NCR (who aren't in a position to create an embargo, because House can essentially turn off the switch that gives them electricity and water). Not to mention, there's an entire running saturnite mine in Big MT as well?
It says in the ending slides that he would keep New Vegas safe and secure for future generations, but if that's not evidence enough, perhaps consider the fact that a robot army is reproducible, doesn't need sleep, food, and doesn't suffer from disease/exposure.
House is going to be very well set up if he wins the dam; the argument that is normally placed in front of Mr. House is whether his "set up" is a good thing for New Vegas and the surrounding areas.