Kasich has particularly broad appeal, especially with independents.  He also polls better with nonwhite voters than most Republicans.  He even goes so far as to acknowledge the fact of climate change, which gives him a leg up with younger voters who aren't fooled by the denialism of the right and who will be living with the consequences of it for their entire adult lives. 

After the dust settles and the magnitude of what Trump has done to their brand sinks in, Republicans will do well to look to Kasich as one of the people who can lead them out of the woods. Nikki Haley is another they should listen to. The problem is the alt-right has infiltrated so deep that they are in an ugly bind: they can't win with this crowd, and they can't win without them. True conservatism is in no way racist (in fact it's anti-racist by nature), but the party of conservatism has dug this hole by not addressing the rot within. It won't be easy repairing the damage.