Without overturning Roe, they will attempt to pass new laws that will make it in practice impossible for many or most women to get abortions. And most of these laws will be 'stealth' abortion bans, laws designed to seem moderate or reasonable on the surface (and therefore protecting Republican congressfolks from voter backlash) while actually banning a wide range of abortion procedures. (The Federal 'partial birth' abortion (PBA) ban is a classic example of a 'stealth' ban; they marketed it as applying only to a single uncommon procedure performed post-viability, but the PBA ban's text could cover a wide range of procedures, mostly pre-viability).
And if the Republicans continue to control Congress, many of those laws will happen at the federal level, meaning that even abortion-rights meccas like New York state will be subject to the new regulations. Contrary to what many people say, the destruction of Roe (whether it's actually overturned, as Amanda expects, or instead whittled down to a shell, as I expect) will not mean it'll be up to the individual states to decide.
Effectively, rather than a few abortion-legal bastions on the coast, the entire map will be red. Clinics that perform abortions will still be inaccessible to all but the wealthy -- instead of being unable to afford to drive ten hours to the next state, they'll be unable to afford a quick trip up to Canada.
It seems the difference between these two possibilities is whether or not the lower-middle-class populations of California and New York are affected in the same way as the lower-middle-class populations of the midwest. While the former populations are large, it's really just more of the same as far as the latter is concerned.