I suppose Congress could create a concept of state-level permanent residence, but even then, if those permanent residents are allowed to become U.S. citizens, then they would be able to freely move to a red state, which the GOP again might find unpalatable. One finer point on this is that if state immigration policies are structured around a skills-based points-ranking, the prospective immigrants would all likely be high-income earners, who are fluent in English. It's an open question if such immigrants (especially, the ones who are not white) would still get treated like an unwanted anathema by GOP-led states.
Quite unlikely. The line would be "California will just let everybody in and send 'em to our state!"