I'd be surprised if federal restrictions go any further than a late-term abortion ban and/or parental notification. They'll be a fight over exemptions for the life and health of the mother, which I think is a politically winning battle for the abortion rights side. I'm not sure how the polling goes on mental health provisions so I won't guess on that. I believe most parental notification laws have an escape clause for abuse or the like. The exact breadth of that escape clause will initially be determined by the political strength of each side.
As the fallout begins to settle, we'll see increasing cases of horror stories from Red States that push the limits on restrictions. Doubtless many will attempt to come as close as possible to an actual ban. At that point, if the abortion rights lobby has its act together, the tide will start to shift back. I tend to think safe, legal, and rare in some form is probably a winning national agenda. Linking up contraception and morning-after pills to lower abortion rates may also be a winner.
There's a popular theory I subscribe to that Roe short-circuited a productive debate in America. The benefit was the achievement of widespread abortion rights. However, the decision had a vital role in galvanizing the rise of the fundamentalist Christianity as a political force. Admittedly, during the civil rights movement and the gay marriage decision in Massachusetts both helped consolidate the rights in question. Roe is probably differet for two reasons. First, the constitutionality of the decision is highly dubious. Second, I think civil rights opposition and gay marriage opposition (at least in Massachussets) was largely a matter of maintaining the status quo. The political balance of power shifted in both cases to maintain those decisions. Opponents were either marginalized by the positive new outcome or were outgunned by the re-enfranchised minority voters. However, those opposed to abortion on moral grounds rather than simply on conservative grounds are a much larger faction. With the decision largely our of the courts and back in the legislature, we'll se if the legislative compromise hypothesis is right.