I think I get it Mr J: You're a yoga instructor! All that twisting and bending has seepted into your consciousness.
Your house analogy is a poor one. It is suggestive of a fixed space, one not intended for expansion. There is absolutely no indication today that the US is "fixed" in regard to an expanding population. In fact a number of countries, such as the UK or Germany, have a much greater population density, yet manage to have an even more livable environment than the US. The UK had a much worse environment in the past, and is doing better today, even with a greater population.
Advances in technology and environmental awareness tend to allow for greater populations than before. Cutting down the forests, and taking a dump in the nearby stream are not the most sustainable practices, but that was all that was available in times gone by. Urbanization is indeed the key fact here, as living in compact and ecologically aware cities reduces the impact on the larger environment- farmland, rangeland, forests, parks and wildlife reserves. Living in compact areas means less expenditure of energy resources for transport, and less cost for providing infrastructure such as water supply, sewage, power lines, etc.
Take the population of New York, and tell them to go out and scavenge at the level of 1804 technology, and they would strip the surrounding countryside bare in a few weeks, in an effort to survive. At today's level of technology though, they do just fine even with densities like those in Manhattan.
You have no "basic fact" here, as the limits of population are uncertain, and changeable with developing technologies. If some of today's green innovations pan out, we may see a future with previously unimaginable populations. Certainly today, the US is a long way from being "full".