No, we're not. Lots and lots of empty square miles to fill and exploit. Perhaps if the government stopped taking land out of circulation, we'd have more room. What have we got now? Cities both restricting land use to maximize "open space" and complaining that they need to control rent because there isn't enough housing.
We're not full up. But I'm certainly fed up with government restrictions and giveaways. The John Smith Rule should be the guide on limiting factor to immigration: "if you don't work, you don't eat". No freebies. No handouts. No coddling. No bilingualism. If they want to be part of America, they need to be willing to play the game our way, and not expect us to help them.