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.
Lincoln Chafee wasn't liberal? Mike Castle wasn't liberal? Michael Grimm wasn't liberal(Grimm voted almost as liberally as Van Hollen in 2013).