My understanding of the social science data suggests that David Brooks gets this odd inversion right:
Among those who are well educated and who are rewarded by the information-age economy, the invisible river reinforces the assumption that childbearing is more arduous and more elevated than marriage. One graduates from marriage to childbearing.
But among those who are less educated and less rewarded, there is an invisible river that encourages the anomalous idea that marriage is more arduous and more elevated than childbearing. One graduates from childbearing to matrimony.
For a vivid explication of this dynamic, you can't do much better than Promises I Can Keep. What, if anything, you do about it is a different question. It's an odd fact that the conservative distrust of Big Government in no way impedes their willingness to promote and demand lifelong marital commitments amongst women whose circumstances, communities, and potential partners they know next to nothing about (but, in other contexts, demonize). Liberals, generally far more content to trust in government's ability to navigate murky sociological waters, tend to shy away from intruding on such a personal and deeply uncertain choice. Rather the opposite of what you'd expect.
That argument aside, it would certainly seem that the demographic fact of single-parent households would spur both sides to create policy such that the disadvantaged children have adequate day care, and health care, and educational opportunities, and all the rest. But the conservative affection for government wisdom on this issue doesn't extend to social policy.
If you're interested, here's a related post on the subject.