Planned Parenthood receives about a third of its money in government grants and contracts (about $360 million in 2009). By law, federal funding cannot be allocated for abortions, but some opponents of abortion have argued that allocating money to Planned Parenthood for the provision of other medical services “frees up” funds to be re-allocated for abortion.

“Some opponents”.

As the saying goes, all money is green. In other words, money is fungible – a concept Wikipedia helpfully links to. If you give me a $10 bill and tell me not to spend it on booze, what are you really saying? That that particular serial-numbered bill should not be used in a liquor store? Okay, I’ll use the two fivers in my wallet for booze, and spend “your” $10 on the food I was eventually going to have to get anyway. And what about electronic money? Dreams about dreams.

Literally the ONLY constraint “no federal funds for abortions” puts on Planned Parenthood, is that the dollar sum of their non-abortion services must be greater than or equal to the dollar sum of federal Title X money received (assuming no other donors restrict where their dollars go). It obligates them to play a little accounting shell game, but in the counterfactual world where PP does not receive federal money, they almost certainly perform fewer abortions; thus, federal funding causes more abortions to occur.

(No comment implied on whether that is good or bad. It is certainly bad from the point of view of abortion opponents this provision is supposed to mollify.)