I am afraid, my view is somewhat pessimistic: the other has simply won the hearts and souls.
It seems to me that the common thread in the message of conservatives is personal reponsibility, followed by the issue-specific refinements. In gun control, for instance, the message is, Do not blame the piece of metal --- it is the criminal that bears the reponsibility for misusing the gun. In dealing with childbearing, do not abort an unwanted child --- accept the reponsibility of carrying it to term and, if it is still unwanted, give the baby up for adoption. In regard to welfare services, do not take support for granted but accept your personal responsibility over your own future and get education, job experince, etc. Similarly, when designing the safety net for the less fortunate in our society, do not rely on the government --- take care of them yourself, in your home and through churches and sinagogues.
Observe that acceptance of personal responsibility leads to more questions than answers, and this is the root of the lesser unity among conservatives. In contrast, an abrogation of personal responsibility can be made by all in the same way. There are other examples of that illustrate this asymmetry. Thus, there are many ways in which one perform work once a job offer is accepted, but only one to decline the offer. And honesty: there are many ways to lie but onty one to tell the truth.
I believe that, in opposition to conservatives, the rejection of personal responsibility is the unifying factor for the modern-day "liberals." It provides for an easy unification since rejection is simple. Once you reject personal responsbility, everything else follows: first damn the country ("make love not war" of the anti-Vietnam protests in 1960s); then damn the parents ("don't trust anyone over thirty"); next the family that you may form ("I don't have to mary; yes, I am 40 and have a girlfriend, but how do I know that I will not meet someone better?"); then damn the children ("It's better for the chidlren if we divorce than if we stay in a loveless marriage"). That's what we saw in the past 40 years: the decline of loyalty to the eternal social institutions --- in the order of decreasing scale: country, community, primary family, family of procreation, and chidren. Only one entity has benefited from this decline --- the self, so prominent in the "me (first)" generation.
These are rather general observations; where does this leave women voters? Recall that it is women who are traditionally endowed with preservation of values in society, whereas males experiment with innovation This appears to be so even in nature: it is the male wolf that goes to a new forrest in search for food, while the female preserves the existing den. Sexually, too, nature appears to endow males with the aggressive role, and it is females that act as gatekeepers and exert the "civilizing" influence on us.
If you accept, at least partly, the foregoing view, then what should happen in a society, such as ours in the 1960s, if it tells its females that they may decline the burdensome responsiblity for children and keeping in check the rather promiscuous tendencies of the males? Predictably, women will no longer be concerned with marriage (they are "equal" to men now, you see; they can have sex without childbearing --- what a great spiritual acheivement!). Liberated from childbearing, they will identify their self-worth with the carreer achievements, just as males did for ages before.
(There is a cost, of course; you cannot fool nature, after all. So, twenty or so years after all these achievements, we increasingly hear about the bilogical clock, etc.; the change, I believe, is slowly coming.)
This helps to offer an answer to the original question. How does one feel when a burden is removed from her shoulders? Happy and grateful. Who advocates the removal of the burden of personal reponsibility? The Democrates in the political arena and various liberal elites in other aspects of social life: on school boards, the academe, etc. Thus, women vote for those who grant then the currently welcome relief. Ditto for Black people, for whom the message of Jesse Jackson and Sharpton is appealing: the burden of personal reponsibility is replaced by the governmental handouts and corporate shakedown.
This premise, if you accept it, is common to both groups and explains why both vote as a block --- for Democrats, of course. Naturally, as the costs of abrogating personal responsibility become clear, more and more Blacks vote Republican and conservative Blacks become more visible: withness, for instance, Mr. Keyes --- a prominent moral voice. Also slowly, the female electorate is becoming more heterogenous as well.
(Incidentally, the foregoing also suggests that the demise of morals is not a result of the pro-abortion legislature; rather, the legislature and moral decline are two manifestations of a common underlying cause. Repelling these laws will not, by itself, bring back the destroyed social insitutions, as some people suggest).
Sorry for what ended up being a rather long post.