The argument I am arguing against is something like:
Immigrants join the labor force -> They increase the economy -> The increase in the economy increases jobs -> More jobs increase wages.
I think this what you are essentially saying?
The problem here is inflation and productivity. In order for everyone to prosper either:
1. There is no inflation and therefore purchasing power is maintained, or
2. Wage growth and interest rates outpace inflation.
No. 1 will not happen under our current monetary system, and no. 2 has not happened due to:
a) Competition in the labor market has keep real wage growth flat, and
b) The unprecedented (in the history of mankind) money creation (AKA Quantitative Easing) used to bail out financial institutions has destroyed interest rates and created a massive inflation in asset prices.
Another factor is that different jobs impact the economy differently. Or put another way, different jobs create different levels of 'value' in society (the monetary kind not moral kind). The difference between the price of a good or service, and the perceived value of a good or service is the 'consumer surplus'.
Fact is, highly skilled immigration is going to create a higher level of consumer surplus compared to low skilled immigration. Highly skilled immigration in areas where there are shortages is going to also have a bigger impact on economic growth.
I think you will be hard pressed to find anyone arguing against this sort of immigration... the issue that dare not be spoken is the impact low skilled and illegal immigration has on the labor market.