(CNN) — On Tuesday, South Carolina Sen. Lindsey Graham introduced a bill that would ban abortion nationally after 15 weeks, with exceptions for rape, incest and when the life of the mother is in danger.

Which leads to an obvious question: Why?

After all, Republicans have been desperately back-pedaling on abortion almost since the moment that the Supreme Court overturned Roe v. Wade this summer, ending the constitutional right to an abortion.

GOP candidates have been busy scrubbing their websites of their more strident language on abortion, which, in many cases, helped them win their primaries, as they see the political blowback in the general electorate.

Recent polling suggests that while public opinion is more split on a 15-week ban compared to the court’s overturning of Roe, which is broadly unpopular, a majority of Americans still opposes the limit Graham is proposing.

And Senate Republican Leader Mitch McConnell seemed, um, less than thrilled at Graham’s gambit. McConnell told CNN’s Manu Raju that he believed the majority of Republican senators would rather leave the issue of abortion up to the states.

The resistance Graham’s plan met almost immediately — and the glee with which Democrats latched onto it — suggests that it may be short-lived.

But it is worth asking: What was he trying to do?

Here’s my theory: Graham sees that his party is getting clubbed on the issue. And some conservative states now have near-total abortion bans in place. Which puts Republicans running for Senate across the country constantly on the defensive, trying to defend a position that is hugely unpopular with the public.

And so, Graham is trying to give Republican candidates something to talk about that he believes threads the needle between keeping the GOP base, which is adamantly opposed to abortion in all forms, happy and not totally alienating the center of the electorate.

Graham is hoping to give Republicans a positive talking point on the abortion issue — something his side can point to as evidence that they are not the intolerant ogres that Democrats have, to date, effectively cast them as in the wake of the Supreme Court decision.

The alternate analysis of Graham’s move is that he deeply believes abortion after 15 weeks of pregnancy must be banned and that his side has to be on the record on it. Period. But while Graham may well believe that, he is far too savvy to simply roll out this plan less than two months before an election without considering the political consequences of doing so.

(Sidebar: The fact that House Republicans are also pushing a 15-week ban — and unveiled it the same day that Graham did — suggests a level of coordination that points to politics being behind all of this.)

Will it work? It’s not at all clear — especially since Democrats control the Senate, making Graham’s gambit somewhat dependent on what Senate Majority Leader Chuck Schumer thinks is the right political move for his side.

The Point: Graham’s ploy is a major flash point in the fight for the Senate majority. It remains to be seen who it helps and who it hurts.