My rebuttal is that this is very similar to what happened in Israel, a large and fairly random ("have some degree of Jewish decent") group of people were allowed to immigrate with very little hassle & it ended up being positive for all involved (except maybe the country they left).
The population of a country already much more densely populated than the US grew by 65% in 20 years[1], so this is not a case of it only working because not many people wanted to immigrate.
To summarize: my opinion is not that there should be 0 filtering, but that there should be less filtering than there is today, and that increasing the amount people coming over would benefit countries like the US and Canada.
[1] http://www.google.com/publicdata/explore?ds=d5bncppjof8f9_...