It would probably just make the issue worse. In some states in the Northeast and West Coast, the world probably re-adopt Roe. In the southern. mormon and agrianiam states, abortion would be a crime and probably handled like substance abuse is today. In the interior west and great lakes, I could see laws a lot like the laws in Britian or Israel today, where it becomes an administrative law issue.
Red= States that govern abortion under their penal codes (The 21 "Right to Life" States)
Blue=States that govern abortion under their administrative laws (The 14 "Wait and Talk" States)
Green= States that govern abortion under their general health care laws (The 15 "Right to Choose" States)
The prodominant effect of this would be that 40% of the population would live in states that forbid abortion access, but only 25% of the population would have no access to abortion.