On this vote the yeas are 50, the nays are 50. The Senate being equally divided, the Vice President votes in the affirmative and the nomination is confirmed.
—U.S. Vice President Mike Pence, 2/7/2017
by Keokani Kipona Marciel, MS Loea Lula Ho‘omalu Kākau Hoʻopaʻa ʻia - Registered Parliamentarian (RP)
Under parliamentary law, a motion is lost if there is a tie vote (or less than two-thirds if that is the required vote).
To maintain the impartiality of the chair, the presiding officer normally votes only to make or break a tie vote. If there is a tie vote, and the chair is indifferent, or wishes for the motion to be lost, he or she can choose not to vote. Since such an abstention does not disclose the chair's position, if any, on the question, the anyonymity protects the impartiality of the chair.
Alternatively, if a two-thirds vote is required, the chair can vote in the affirmative to make a two-thirds vote, or can vote in the negative to lose a two-thirds vote.
Also notice, in the video clip, that after the result of the confirmation vote was declared, the Senate Majority Leader, after obtaining the floor, immediately made an original main motion to Reconsider the vote, which can only be made by a member of the prevailing side.
He then followed this by a subsidiary motion to Table the motion to Reconsider the confirmation vote, which was carried.
Finally, he asked for unanimous consent to waive the mandatory quorum call, which is an incidental main motion to Suspend the Rules, requiring a two-thirds vote under general parliamentary law. The chair confirmed unanimous consent by saying "Without objection." This means that opposition to the motion, if any, had acquiesced, since a single objection would have compelled a vote. However, this could have been viewed as dilatory, potentially making the opposition look bad.
The motion to Table, under the procedural rules of the U.S. Senate, is different than the motion to Lay on the Table under general parliamentary law. In the former case, the motion to Table has the same effect as Postpone Indefinitely under general parliamentary law, which is to kill the motion.
Why did the Senate Majority Leader move to Reconsider, then to Table that motion?
By killing the motion to Reconsider the vote on the confirmation, it prevented that reconsideration from again being moved by a member who voted in the affirmative. By making this motion as soon as possible after the confirmation was declared, it minimized time for contemplation of the motion to Reconsider, thereby making it easier for the motion to be tabled by a majority vote.
Why did the Senate Majority Leader ask for unanimous consent to waive the mandatory quorum call?
In theory, it is possible that enough opposition members could have exited in time for the assembly to lose its quorum, and possibly jeopardize the validity of the confirmation vote. Given the sustained opposition to the confirmation, nothing would be out of the question. Therefore, by making this motion immediately after the confirmation vote, it would minimize the time available for senators to make an exit.
In any case, the series of three motions made by the Senate Majority Leader can be seen as a formality to make it clear for the record that the confirmation was unequivocal.