They're going to have to suffer a few bad elections as the base adjusts. It's the only way to survive a demographic change. Or just lay off the anti-immigrant shit and they'd discover how socially conservative Latinos can really be.
I think that's the far more realistic tweak. Aren't Latinos and a lot of African Americans actually pretty conservative in a decent number of ways? They won't have to drastically change much if they can just highlight those things and move from there.
But then again, I think a lot of that is social conservatism, and so that'll probably always be on the decline, though they can take advantage of it for a little while.