A common criticism about the newest generation of immigrants is that they are detracting from the national identity. This isn't a fringe claim (or even a new one, really). Acclaimed political scientist Samuel Huntington's book Who Are We? argued that Latino immigration posed "a major potential threat to the cultural and possibly political integrity of the United States."
It's hard to have much sympathy for the argument that policymakers should turn back the huddled masses, especially at a time when (1) the United States' internationally superior higher education system attracts some of the world's smartest students and (2) we should be focusing on ways to build the younger sections of our tax base to help pay down our guaranteed expenditures to older Americans.
Still, the makeup of America's immigration pool has changed dramatically in the last half century. Europe's share of total immigrants in the last 40 years has fallen from 60% to 13%. Mexico, the Caribbean and Latin America have grown from 19% to more than half of all immigrants and Asia's share has tripled (via Brookings).