Current law seems to* guesstimate state-by-state about how late in a woman's term a fetus suddenly turns into an unborn human, and sets laws based on that. It's not perfect, especially seeing as how you never know exactly when the term started, but it's a sight better than a lot of the alternatives that have been offered. Personally I'd like to see it boiled down to having a qualified - perhaps even specially licensed - professional make the call on whether the fetus is externally viable or not. As it stands now you're basically relying on a specialist anyway to judge how long the term has been, and depending on his or her professional standards they could slide the number either way.
There seems to be a terribly complicated set of parameters in place to determine whether or not the procedure is publicly funded or not, and I've got mixed feelings about that. I disagree with a lot of what Sora just said but I do feel it ought to be treated like any other insured surgery, but that blocks out a lot of lower-income people who honestly tend to have the most compelling reasons to get it done. I like to encourage abortion whenever possible - not exactly because I'm a baby-killing monster, but, well, if you really want me to go into it again, ask me. Anyway putting a monetary barrier in place isn't going to help anything at all, but I don't advocate treating it any different from, say, a heart replacement in the end.
Perhaps it would be best to reclassify abortion from 'elective' to 'urgent'. Once you get past the semantics of it, it makes more sense - it's not like you can put it off until next year.
* It's a little tricky to get solid information on.