couple thoughts:
1. historical: nearly all cultures who have ceased or prevented immigration have gone through periods of stagnation and/or even collapse, such as the Chinese, Japanese, Romans, North Korea, etc. Convsersely, countries who consistently lead the world in technology and economy are most liberal in immigration policies (the US, the EU, Hong Kong, etc.)
2. Overpopulation: for years, the idea of overpopulation has been a common sense argument: more people must be bad, right? but in reality, more people has never resulted in worse living conditions. a certain percent of the new population are farmers, sanitation workers, scientists, etc. and consistently, the production of each person exceeds their consumption. therefore, immigration increases overpopulation, which in itself, is not as bad a thing as we are led to believe.
3. the 3D argument: as an economy becomes more and more advanced, fewer and fewer of the people want to do the "3D" jobs: Dangerous, Dirty or Disgusting. However, if nobody does these jobs, the civilization will collapse. Immigrants, because of language and cultural barriers, are often well-suited to and much more likely to take these jobs. An argument could be made that without immigrant slaughterhouse workers, for example, we couldn't make Dior handbags.