No, he doesn’t have time before the midterms to get a replacement in. But if they turn Kavanaugh down, and if the Senate gains Republicans, then they will get a replacement even better. If the Republicans lose the Senate, the situation will be very bad. The seat may sit empty for 2 more years.
Just to add to my last post:
So, people like Collins and Murkowski may understand that logic. If they turn Kavanaugh down, they end up with either Barratt, who they like even less; or with a situation where the seat sits empty. Trump will not pick a Souter just to get him through the Senate.
By October, it will probably be evident that the Republicans will gain seats in the Senate, and the holdouts will come along.