Immigration can be a tough issue for progressives. On the one hand progressives tend to believe that government, and society at large, should work on behalf of the people. A progressive could very easily end up on either side of the immigration divide. They could take a no one is illegal stand and fight for illegal immigrants rights in welfare, health care, and employment. On the other hand a progressive could look at immigration through a strict class lens and see its economic function solely in deflating wages and lowering the living standard of American workers.
Immigration has a long history in the United States, not all of it pretty. For as much cultural pride we have in our immigration myth, its economic function has always been to destroy unions and lower living standards. Unregulated Immigration is free labor, the opposite side of the coin of free capital. Immigration today has an identical economic function as free trade.
An economic progressive stance is one that rejects the wage deflation of free trade and free labor. It is not progressive to flood a labor market with free labor when it has fought for years getting unionized. Even if we agree that our government bears responsibility for this immigration mess, the current immigration levels are not sustainable.