The legislature has dealt with this issue by passing strong, specific laws regarding abortion in many of the states - with quite opposite conditions depending on the state. And it's not because of lack of "rotating" politicians, quite a few of them got elected on because they promised to prohibit abortions, getting votes from the state majority of conservative voters who considered a strict prohibition entirely appropriate.

The federal legislature, on the other hand has it a bit trickier, because despite the much grown influence of federal government using the commerce clause, it does technically seem that this kind of policy is something that according to USA constitutional principles gets to be decided on a state level.