What? Like I said, all existing checks and balances are still in place. I won't be getting a vote in the Senate, and the senators will still debate and vote on bills as usual.
In any case, my second-in-command already has a casting vote and various administrative duties in the Senate, so I'm not sure what aspect of the separation of powers you're concerned about now.
I'm concerned that the power of the president is to put laws into action, not to write them, adn this fundamentally changes that.
As for the VP, his vote comes from his position as President of the Senate, not as VP.