I'd noticed the same thing, and can't recall what Rush said, if anything, during W's two big amnesty pushes during 2006 and 2007. And I've heard little or nothing from Rush about TPA and TPP.
But Rush did come out in support of NAFTA and did everything he could to discredit Perot, whose opposition to NAFTA was one of his primary issues. Rush seems either to support the GOPe on immigration and trade, or has very little to say. I've concluded that Rush is and always has been GOPe on immigration and trade issues, and most all issues.
He made his name deconstructing liberalism and talking in general terms about conservatism. Have listed to him very little for several weeks now.
The jury is in Rush was in the tank for the establishment all these years. I am sadder but wiser.