It's an ordinary vote, so a majority of those voting or a tie with the veep deciding the issue is sufficient. That said, unless it looks like there would be a lengthy vacancy, I'd like to think the Senate retains enuf collegiality that it would resolve the situation so as to reflect who would likely get the post when all seats are filled.
Exactly. Most likely with such a small majority either way, there wouldn't be any real shift in the actual agenda before the body, so there would be little reasons to go back and forth over a set of possibly only days.