Just remember, they have been pouring in for twenty years and their have been no GOP efforts to do anything. In other words, playing politics with this diminishes the problem.
The biggest GOP related effort is that by Grover Norquist to block any possibility of Congressional cooperation with his no new taxes pledge. I have a son in Afghanistan and fear what this is doing to funding for our military. Others here at FR have been worried about his links to Islamic organizations, his Muslim wife, and attempts to get some into the government. Put “Grover Norquist Muslim,” or “GN Islam” in the Search box. When the page comes up click Archives for back articles. Pretty scary stuff there.
I did this search when with considerable surprise I heard him a few days ago urging quick passage of an Immigration bill. Is he worried that with the Tarnaev brothers we may make it harder for Muslim immigration?