The House has no role in confirmations. But I do hope Democrats do something stupid and unhinged like trying shampeachment again. Let the American people see that right before the election.
In addition to believing that nominating a candidate to replace Ginsberg is an impeachable offense, they are going to make the stupid and/or crazy leftie base believe that impeaching Trump would somehow invalidate his SCOTUS nominee. Of course we know that isn’t the case. Even if by some real with the devil the Dems manage to muster 67 Senators to vote to remove Trump, his pick remains on the bench. Bottom line: Pelosi has no power to affect this pick; just make the pick and get him/her confirmed and let the loonies on the left throw their tantrums.