What do we think this is about? Why single women in particular? Republicans generally favor a set of national values and institutions that presume most individuals live in married households. Unfortunately, this is less and less true.
Democrats' view of government is in loco parentis, Latin for in place of parents; meaning the government will care for you. This Democratic view is particularly appealing to groups which, in one way or another, feel threatened or abused. Some (but not all) racial or ethnic minorities, non-typical gender orientations, the very poor, and single mothers all fit this profile.