Literally every time that abortion has been on the ballot, Republicans have been victorious. A supermajority in the country support a 15 week ban, which is why Democrats have to lie about it.
The bill's passing is somewhat irrelevant, because there's no way in hell Joe Biden would ever sign it. What Lindsay Graham is doing is reminding these rabid anti-abortion Republican voters, single issue voters, that they better vote even for the most shitty of RINO candidates in November. Because if they don't, and Democrats win in November, they will almost certainly move to legalise abortion at the federal level and make the Dobbs decision moot.