Reductio ad absurdum. Try again.
The current United States population growth rate is the very next best thing to the definition of "sustainable". What you seem to fail to realize, or perhaps willfully ignore, is that by the very way immigration policy works, the legal growth rate cannot and will not grow significantly. The absolute number of people, obviously, will increase, but the rate as a percent will not now or barring very significant reform change in either direction. Furthermore, the land area of the United States being used to produce crops is over 40% of the available landmass. That's over 1.5 million square miles. Over 1 billion acres. That's as of now. But where does all of it go, you ask? Over 25% of the corn crop is used in ethanol production alone. Millions of tonnes more crops are used in commercial applications, or other non-foodstuff functions. The farmland available in the United States right now could comfortably feed 500 million, 800 million, perhaps even yoru hypothetical billion people. Even taking the argument to it's (il)logical conclusion, there is very little legitimate threat in the form of population growth.
Also, I feel the need to remind you that, assuming 1% growth annually, compounded continually, it takes 72 years for a population to double. That means it will be well over 100 years before the U.S. even conceivably reaches 1 billion population, by which point the infrastructure damn well be in place, or the failing isn't in the population sector.