To be clear, as the new prez Harris could nominate anybody she wants to as her VP, BUT that person cannot take office and be the tie-breaking vote in the Senate until AFTER he or she has been confirmed by the Senate and the House. And neither can Harris, once she assumes the presidency. So, we have 2 basic options:
1. Harris nominates Senator Warren or another senator to be the new VP. I am not sure if Warren has to resign from the Senate in that event, and be allowed to vote for her own confirmation or not. One would think not, but I don't know the law on that. Certainly that would not be well-received by everybody else who is not a democrat and maybe not even all of the democrats. But what I do know is that even if she could vote once, she won't be able to vote for herself twice; once as a senator and once as the new VP, for the simple reason that she won't be the new VP until AFTER the confirmation vote and she takes the oath of office for VP. Either way, the democrats would not have a pathway to 51 votes in the Senate. Remember, as the new prez Harris does not get to vote.
2. Harris nominates a non-senator, be it Pelosi (unlikely) or anyone else. At that point , Harris is no longer the VP and does not have the tie-breaking vote. So, the best the democrats could do is 50-50, and a majority vote is required or the confirmation fails. UNLESS some fuckwad RINO sides with the democrats.