The Republicans may seem to be driving things, but they have no good hands to play, it is least bad. If they vote without having heard Dr. Ford and the multiple contemporaneous witnesses still emeging, and Judge who was there, the GOP will pay the price with women for decades.
An even more interesting question is: do they really want to overturn Roe v. Wade? Judging by extensive polling data stretching back decades, it's doubtful whether any action is more certain to render Republicans permanent political pariahs. Best way for them to lose by winning.