"I don't think we'll be able to overcome this problem unless we restore the social norm of not having sex and not getting pregnant before marriage," said Peter Sprigg, senior fellow for policy studies at the Family Research Council.
Social conservatives do not generally support research about social norms about sexuality, so we do not know as much about sexual norms as we would otherwise. According to the earliest representative studies by sociologist Ira Reiss, the attitudes to allow what Ira Reiss called "permissiveness with affection" started shifting in the 1940s, and the shift was well underway by 1950 and definitely by 1960 when Ira Reiss wrote Premarital Sex in America (the link goes to the actual book). It seems unlikely that such a long-standing attitude shift could be easily reversed. By now, it is the standard that even many Evangelicals follow. If they marry right after college, it's possible they may abstain, but if they marry later, it's very unlikely, and many do marry later.
I would argue that permissiveness with affection is not a policy issue. No public health problems result from premarital sex within long-term committed monogamous relationships. Disease spread is self-limiting. Still, if changing that social norm is a worthy public policy goal, they have to look to more recent trends first.
One norm that has changed more recently are attitudes towards what Reiss calls "permissiveness without affection:" just as AIDS was emerging in the early 1980s, academics were declaring this to be the new norm. From the poll data in the link (which I would guess is an incomplete picture of the available data), it looks like endorsement of the norm may have declined with AIDS/HIV, and has begun to reemerge to some extent and even become part of public discourse, with everyone having heard of the idea of "Friends with Benefits". Unlike permissiveness with affection, there is some degree of a public health justification due to the herpes and HPV risks.
But that means you have to acknowledge that that nearly all Americans have premarital sex, and teach real sex education to protect them.
And then you have to think of a policy that can change social norms. Incidentally, changing social norms would seem to be totally inconsistent with a limited government of the sort that Conservatives say they want.