If the Democratic party were more lenient on abortion I am sure they would pick up another 20% of the Evangelical Christian vote at least. I personally know dozens of Evangelical Christians who are generally left wing in regard to taxes, welfare, the Iraq War, etc., but are also pro life.
The majority of the country, though, is "pro-choice", depending on your definition. (The majority of the country is also perfectly comfortable with limiting abortions through such measures as requiring parental notification, for example.) What people are uncomfortable with in the way you suggested, I think, is abortion itself as opposed to its legality.
Really, as pro-choice goes, there are a lot of people such as myself who consider ourselves pro-life, yet who favor legal abortion in special cases. So this inflates the pro-choice numbers artificially....