One effect - economic conservatism may make a comeback.

NY, CA and several other liberal states tend to have people who call themselves "conservatives" (folks like me). We tend to be libertarian leaning economic conservatives who don't identify with religious culture war stuff (war on christmas, the gays are gonna get you).

We get ignored since our vote doesn't matter. This leads to national candidates who are basically Democrats with a little bit of Jesus thrown in (e.g. Bush, Romney), albeit answering to different special interest groups.