The Constitution gives the vice president no power whatsoever over the states. In fact, the Twelfth Amendment gives him no authority to do anything other than “open all the certificates” by which the states have individually certified their electoral votes. It doesn’t even say he gets to count the votes. After directing the veep to open the certificates, the amendment goes into the passive voice: “and the votes shall then be counted.”
That is because the task is entirely ministerial, as is the vice president’s participation. Yes, it is solemn. After all, a presidential election is being certified. On such an occasion, the Constitution aptly calls for a joint session of Congress, led by the veep in his capacity as presiding officer of the Senate. But Congress is in the role of witness, not judge. Pence and the federal lawmakers are there to observe each sovereign state’s formal certification of which candidate has been awarded its electoral votes, and the tabulation by which the states collectively elect the president.
In fact, under the Constitution, the Senate and House do not even certify the result.