The United States has always relied on immigration from worse-off countries to grow strong as a country. The immigrants come here and become Americans. Only a minority of today's Americans are descended from immigrants from Britain (indeed, only a minority of my own ancestors were from Britain), but almost everyone here is English-speaking and American in cultural outlook. This is how immigration works: people become acculturated to the new country, even with very high rates of immigration.
I would speculate that it won't work anymore. When economy is bad and only unsustainable wages are available for work, immigrants will stop assimilating and start to create 3rd world within 1st world. I think it already happens.