Do they?
This much I am certain of -- the majority of voters are politicallly conservative.
It's the 'social' issues that chase many people away from voting R.
Many socially liberal people vote D cuz they don't like the social Cs angle. But like with Reagan and with the contract with America, when a person comes along who promises not to push the 'social engineering' policies but instead focuses on the 'political C' ideas of govt accountability, etc . . . then we find out that the vast majority of Americans are politically conservative.
The problem is by far most people, on social issues, are "live and let live". And the social Cs agendas against Gays and such scare many, many voters away from the R party.