I posted this earlier this month on another board, but it seems appropriate here as well.
One place where the labels don't fit well, and where the GOP has seen its biggest losses are in the suburbs. The suburbs were a big part of Reagan's coalition, and he knew the importance of their issues.
The biggest issues in the suburbs are what I would call quality-of-life issues. They don't like taxes, but will accept those that go to core services like safety, infrastructure, and basic education. The suburbs can deal with social change but preferably in small incremental steps. Radical change is frowned on, but so are attempts to turn back the clock. Environmentalism is important, precisely because it has a strong link to the sense of quality of life and it too is subject to the incremental approach.
I would not characterize this as liberal in the urban sense, but it doesn't find an easy expression in modern conservatism. To mount a comeback, the GOP must find a way to show how this fits within a conservative view as it had for decades.