I hate this fake liberal nationalism about "American values." As if hypothetically America had never allowed immigrants you would be fine with keeping it that way. You want more immigrants because you want more immigrants, not because it's "an American tradition."
Me, I don't even pretend to be a nationalist. A country is only as good as the life it provides to its citizens.
If we allow immigrants in at the rate we do, our standard of living will remain the lowest in the first world.
Also, you're confusing the issue by bringing up refugees, which are a totally different issue from economic migrants.
I don't feel the two are separate issues at all. Certainly the debate last year about the Guatemalan refugee children in Arizona was treating them like economic immigrants despite their fleeing the most violent society in the Western Hemisphere looking for a new life in a society where they wouldn't have to worry about getting murdered in their sleep. Alternately, look at the coverage of the boat peoples in the Mediterranean, very little of which mentions that most of those immigrants are refugees from Eritrea and South Sudan, two of the most horrifying places in the world today with huge refugee crises. The talk about the people from Syria dislocated from their homes ends up with a lot of language about "not wanting them here" as well.
I don't feel there's anything "fake" about my championing of immigrants coming here. My great grandparents fled Russia with little in the way of talent and no English and thrived on this side. I will never, ever sympathize with anyone whose arguments would have locked the door to this country to them. It is a bright line for me, a position that betrays that the person holding it is utterly incompatible with my core values and principles.
Frankly, it is far, far more important that people are able to live without fear of getting gunned down in their sleep or murdered for being considered the wrong ethnicity in a civil war than what average wages and benefits are in this country. This country has always prided itself on being, to quote Cole Porter, "the kind of a nation/where people go from Poland to polo in one generation," and that upwards mobility of people considered the impoverished refuse of the Old World into the comfortable class at the core of the United States is the very premise of what the American Dream is.
By the way, how dare you call my beliefs "false" in your opening sentence, as if you're implying dishonesty here. I've made it clear for years that a more open and welcoming immigration policy is a primary focus of mine, far outstripping wages or health insurance or pensions or anything else. It's pretty close to my #1 issue.