According to a study by Emory PoliSci guy Alan Abramowitz, the Republican base is primarily white, married and Christian. These are also three groups that are decreasing in the electorate:
Married white Christians now make up less than half of all voters in the United States and less than one fifth of voters under the age of 30. The declining proportion of married white Christians in the electorate has important political implications because in recent years married white Christians have been among the most loyal supporters of the Republican Party. In American politics today, whether you are a married white Christian is a much stronger predictor of your political preferences than your gender or your class -- the two demographic characteristics that dominate much of the debate on contemporary American politics.
We are becoming less white, less married, and less Christian. This makes the future problematic for the Republican Party, unless they reach out to this constituency. But this group tends to hold much more liberal positions on many issues including abortion and universal health care, so chances are that any efforts to reach out to liberals will be checked by the conservative base. Will the party be able to manage this problem? Is the problem misdiagnosed?