Two points. First, a valid comparison in US to EU as a whole (entities of the roughly same size) rather than individual EU countries. EU has a much greater population density than the US, but also larger immigration than the US. It is only recently, especially after 9/11, that some of the nasty immigration policies started to emerge - and they are clearly a response to militant Islamism. Most reasonable people want their government to protect them from terrorism and overpopulation - even if that translates into tightening their traditionally liberal stance toward immigration.
Secondly, US immigration policies were seldom an act of compassion - they either served to alleviate labor shortages and to undermine labor unions, or political propaganda (esp. immigration from the Soviet Bloc countries).
Wojtek