I don't have the statistics in front of me, but virtually every poll I've seen has said that the majority of Americans want to seriously reduce our level of LEGAL immigration also. Whats most interesting to me about the immigration debate is how it skewers the usual Left/Right dichotomy. The elites on both the Left AND the Right are all for endless Mass Immigration. With the vast majority of Americans in the middle VEHEMENTLY against it.
The Limosuine Liberals on the Left, their hearts bleed for all "minorities" (so long as they don't have to actually live amongst them). And the Corporate Conservatives on the Right see endless millions of new immigrants as nothing more than cattle to feed on: an endless source of cheap labor and millions of new consumers to buy their crappy products.
What a strange issue this is: immigration.
"Americans want to seriously reduce our level of LEGAL immigration"
The context that I think Americans support it is when there is a prerequisite for some needed skill or trade. I don't believe that is the criteria for immigration today, so I can beleive what you say.