I thought Grassley was the Judiciary Committee chair?Graham is unfortunately the relevant one here. He is the chairman of the Judiciary Committee, and he can stop this single handed if he wants. McConnell can't get it to the floor without him. Lindsey is on record as saying he will not advance a SC nominee in the last year of Trump's term.
Two relevant factors here:
1) Lindsey is a damn liar.
2) Lindsey's seat is... not secure, for the first time. He needs to know how this is going to play in S.C., because he is sitting on razor thin margins right now, and needs to know which way the needle tips on this one.
My guess is that he won't want to advance it through committee until after Nov. 3. They will ram this one through in the lame duck session. He has zero integrity, but he does want to win reelection, I think both he and McConnell will prefer this as a carrot to dangle.