SoCal ping
While I certainly don’t agree with his fear of Palin premise, the VP doesn’t run the Senate. Ask John Adams. The VP has no power whatsoever except that breaking a tie vote. The VP is the executive branch and that’s been decided and is as clear as crystal.
However, her point was much more, “I will be active and work for the Executive Branch with the Senate” answer than saying the VP was “in charge of the Senate”.