No, we're talking about AUTHORITY, as explicitly delegated in and by the Constitution. Congress has no authority to adjudicate presidential Electoral disputes because the Constitution doesn't give it any.

"Due diligence" means following the Constitution. Congress attempting to usurp the law to wield power it is not authorized with, would be the exact opposite of due diligence. Same applies to the President of the Senate.

If you don't like what the Constitution says or doesn't say, then your problem is with the law. Work to get it changed. But don't lie about it actually says and doesn't say.