The Constitution says nothing about entertaining objections from the floor, so that would have to be a matter of statute. That's the only role the process in the 1887 Federal statute plays here -- and I have said here on several occasions that some key provisions of that statute are clearly unconstitutional.
Interestingly, once an objection from the floor is "heard" and recognized by the VP, the VP has less power than anyone else in the room -- because he can only vote on any matter if there is a tie in the Senate chamber.
... and is fully empowered to count what he wants ...
Can you cite a single shred of evidence to support this -- either in the U.S. Constitution or in any Federal statute? Maybe it's just me, but it seems absurd on its face.
It’s just you. Robert Barnes, John Eastman, and many others have argued the presiding officer of the Senate (see senate rules) can entertain objections from the floor at any time.