In the advice and consent process, should the minority party refuse to participate in a floor vote and the majority has only 50 members, can the vice president's presence for a vote create a quorum?
The Vice President is not a Senator, and so may not participate in quorum calls. The constituion calls the VP "President of the Senate", but states that "The Senate of the United States shall be composed of two Senators from each State". Thus the VP is not a senator. If only 50 Senators and the VP are present, then a quorum does not exist.
However such a strategy is unlikely to succeed. The Senate presumes quorum unless a Senator suggests otherwise (even when it is obvious that fewer than 51 Senators are present). If a party has 50 Senators then they simply don't suggest that a quorum is not present, and no roll call is taken. The Senate can continue its business without interuption
If a quorum count is demanded, and fails, the Sergent-at-Arms can require Senators to attend, if necessary he can arrest Senators to compel them to attend:
If a quorum fails to vote, the Senate can, by motion, direct its sergeant at arms to compel the attendance of absent Senators or even to arrest absentees in order to establish a quorum. [see Riddick’s Senate Procedure, pp. 214-224] The Senate rarely finds it necessary to take this step. Senate rules and Procedure
- A quorum shall consist of a majority of the Senators duly chosen and sworn.
The Vice President is not defined as a Senator in "PRESENTATION OF CREDENTIALS AND QUESTIONS OF PRIVILEGE" section of the rules.
The Vice President would be precluded from participating from quorum call votes.