One issue that has come up a lot in the discussion of expanding immigration is many people's worry (at times, I have been one of the worriers) about immigrants coming in and voting, more than existing Americans do, for statist policies.
There have been many discussions of this on this blog. I'm on a flight right now and I don't want to take time to find the links, but if you check for work by Alex Nowrasteh, cited on Econlog and elsewhere, you'll find such discussions.
I'm finally getting around to reading Daniel Okrent, Last Call: The Rise and Fall of Prohibition, and what do I find pops out at me in the first part of the book? The fact that immigrants in the 19th century were a bulwark against Prohibition. Okrent writes:
The opposition of Portland's Irish community could have been seen as an augury. For the next three-quarters of a century, immigrant hostility to the temperance movement and prohibitory laws was unabating and unbounded by nationality. The patterns of European immigration were represented in the ranks of those most vehemently opposed to legal strictures on alcohol: first the Irish, then the Germans, and, closer to end of the century, the Italians, the Greeks, the southern European Slavs, and the eastern European Jews. But the word "ranks" suggests a level of organization that did not exist among the immigrant populations in whose lives wine or beer were so thoroughly embedded. Only the German-American brewers showed an interest in concentrated action, when they united in response to the imposition of a beer tax during the Civil War.