The "Liberal Republicans" died long before the "Conservative Democrats" did. The last GOP Senator that I would describe as a "liberal" was Lowell Weicker. The last GOP Representative I would describe as "liberal would be Chris Shays.
If this type of Republican couldn't win the GOP nomination at a time when the GOP base was in New England, how will Baker win in 2020? Or ever? Religious conservatives will veto Baker on the ticket in the same manner that Big Labor vetoed Jimmy Byrnes as FDR's VP in 1944.
Would Governor Phil Scott of Vermont be a "Liberal Republican"?
I would say he's kind of like me: socially moderate while economically conservative. I read something awhile back that said his economic beliefs are essentially what tie him to the party.