The decline in abortions is no thanks to Obama.
What makes you think that? The rate at which people get abortions is based on a wide variety of factors. The very first factors to consider are the rates of unwanted pregnancy. Using teen pregnancy as a proxy for that, it appears unwanted pregnancies have dropped a great deal on Obama's watch. In fact, they're the lowest they've ever been in American history.
Towards the end of the Reagan/Bush socioeconomic disaster (when a whole series of conservative initiatives backfired leaving us with epic social problems), we hit an all-time high for teen births, and that rate has now fallen by over half. And that's not because of an uptick in abortions, since, as I pointed out, abortion rates have been falling fast.
Obama has pursued a number of policies designed to lower rates of unwanted pregnancy, including moving away from the counter-productive abstinence-only approach, and trying to make contraception more affordable by covering it in Obamacare plans. I assume you believe Obama's efforts had nothing to do with bringing about the very outcomes his efforts were designed to bring about, and that it's a mere coincidence that things have been improving so much lately, after having gotten so much worse in the Reagan/Bush years. But, that's the choice voters have in November 2016. If a Democrat is elected, they'll get desirable results. If a Republican gets elected, they'll get an army of earnest people explaining why it's not fair to blame the bad results on the president.
Anyway, preventing unwanted pregnancy is only one factor in reducing abortion. When unwanted pregnancies do happen, a woman has a choice to make, and it matters what the factors are that go into that decision. If she foresees a future of crushing poverty, in which she can't possibly support her child, or even feed it properly, abortion will look more tempting. If she foresees a future where Uncle Sam has her back, and at a bare minimum she can count on being able to afford nourishing meals and high-quality healthcare, she's going to be more likely to decide to take that unwanted pregnancy to term. It also matters whether she's facing a "slut shaming" culture, or a supportive one. If the surrounding culture is one that treats single moms as monsters, and which treats non-procreative sex as shameful, it's going to be tempting to abort that pregnancy before anyone knows about it. If the surrounding culture is not that intimidating on those issues, though, that temptation will be lessened.
There is a strong tendency for right-wingers to focus unproductively just on the pipe-dream of punishing women who flout their sexual taboos, rather than doing things with a reasonable chance of actually lowering the abortion rate. I'm a practical guy, so if I were eager to lower the abortion rate, I'd look at things that seem likely to do so, like lowering unwanted pregnancies and supporting single moms and poor families. But that's just me.