The (accurate) picture I painted was one of a nation that has no political will to do such a thing. I would also add, though, that sustaining a healthy per-capita GDP would be difficult even under the no-growth scenario you described, because increasing efficiency in any sector of the economy is more likely to pay off if it results in higher output, not the same output for lower costs.
Interestingly, what now defines the difference between the U.S. and Europe is that they are somewhat "ahead" (I use that term loosely) of us when it comes to dealing with their looming demographic problem -- they have no apparent problem killing off their senior citizens when they become a burden on their public health system.
Continual advancement of technology will increase output over time...this has been proven over and over again. Someday machines will make machines with very little human involvement in the production process. It's already happening.
Moreover, and I think you might agree, there is a theoretical limit to which our planet can support our global population. Resources are finite and even with our technology we human beings still are subject to the laws of nature and cannot crowd out other life forms we are dependant on for our survival--without consequences. Until we progress our technology to the point where we begin colonizing other planets in the galaxy there is a natural population limit (somewhere) to our species. For all we know, we might have already exceeded it, and nature is in the early stages of addressing it.
I agree with you that the political will to address the immigration crisis is lacking and little will be done on this front unless and until the American People demand a change and hundreds of politicians lose their jobs over their stance on this issue. Stay Tuned.