Can be summed up in this Dummocrats post.
I think most people mistake this as some sort of race/national identity issue. It isn't. Most Americans today are proud that this country is a destination, and most are proud that they themselves are a product of immigration. But they do want our citizens to prove they really want to be here. In the 1800's, being willing to risk disease or death over a long trans-oceanic journey was pretty good proof. Today, standing in line to earn citizenship is a much safer stand in for most Americans. If you opened up immigration for unskilled labor and fast tracked the citizenship process, this would barely be an issue because most Americans would find this abundantly fair. What most Americans DON'T want is for this country to be an escape hatch for another country's undesireables, and I find that to be abundantly fair.