As the stigma attached to unwed motherhood has diminished, the United States has seen both a huge increase in the proportion of babies born out of wedlock -- now reaching almost 37% --and a striking decline in the incidence of abortions.
In 1981, 29.3 abortions were carried out for every 1,000 women of childbearing age in the United States. By 2005, that rate had tumbled to 19.1 per 1,000 women.
The experience of the Palin family symbolizes the effect of the pro-life movement on American culture: Abortion has been made more rare; unwed motherhood has been normalized. However you feel about that outcome, it is not well-described as either left-wing or right-wing.
I'm obviously not the most trustworthy person to evaluate these claims, committed as I am to the goals of reducing and restricting abortion and shoring up the two parent family. But again, I just don't think this argument holds up. There is a correlation, seemingly, between the teen birth rate and the abortion rate, but it's roughly the opposite of what Frum and Weisberg's argument would suggest - the two rose together into the Nineties, and have basically declined together since. Meanwhile, there's no obvious correlation at all between the abortion rate and the out-of-wedlock birth rate: The two rose in tandem until the beginning of the Clinton era, at which point the out-of-wedlock birth rate continued to rise, but more slowly than in the '70s and '80s (see Figs. 12 in this report), while the abortion rate fell precipitously - too precipitously, I think, for the post-1990 increase in out-of-wedlock births to account for the post-1990 drop in abortion, though I'm obviously no statistician.
As I've written before, I suspect that serious restrictions on abortion would lead to a short-term increase in out-of-wedlock births (and thus any serious pro-life politics would have to accept the need for serious experimentation with the American welfare state in response to the challenge). But my supposition is just that - it's unsupported by the existing evidence, which suggests that the relationship between abortion law, sexual conduct, and out-of-wedlock births is far more complicated than any simple "more abortions = less illegitimacy" equation. That equation was plausible in the late 1960s, and indeed represented an important line of argument for advocates of legal abortion. But the evidence of the last few decades hasn't been kind to it.