You want to intensify our culture's already broad, deep strain of sexual Puritanism, shame and blame, and attach it to contraception. It won't work, because contraception is really about other values—pleasure, health, self-expression, self-protection. It comes from a different part of the national soul, the anti-Puritan side that says sex is good, has many meanings from sacred to silly, is a natural part of life, and that women should not pay a price for having a sex life. Anti-choicers mostly don't have this view, and that is why they aren't so keen on birth control despite the obvious fact that blanketing the nation with contraceptives would lessen the rate of something they consider to be outright murder.
And that is why there is no movement of pro-Roe abortion-hating contraceptive enthusiasts, just waiting for Barbara Boxer to sound the trumpet.
Even aside from pro-lifers lots of people are uncomfortable with their sons and daughters having sex. Programs to provide easier access to contraception involve providing easier access in high school and colleges. Access to contraception just doesn't have the universal support that people like Saletan imagine. It's a regular controveresy in high schools and in colleges. People associate contraception with sex and associate easy access to contraception with easy access to sex. A big chunk of this country also thinks "sex is icky" and doesn't like the idea of "easy access to sex" for unmarried people.
Of course married women have a large number of the abortions in this country and expanding contraception availability includes them, but contraception availability implies availability for everyone. That just doesn't make everyone happy, actually.