Just hypothetically, suppose, just suppose, that everything is so snarled up by Jan 20, that no clear winner can be declared.
At 12 noon, Trump and Pence’s terms expire, Neither Bide nor Trump can be sworn in.
Next in the line of legal succession is... is... is...
Nancy Pelosi!
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First she would have to re-elected speaker of the house since all terms end on Jan 3.
Second, various legal eagles have pointed out that the order of succession, depends on a President & VP having been sworn in and some subsequent happening to both.
It does not apply to a situation where none has been elected and sworn in. In that case, it would go to the President Pro Tempore of the Senate until things are sorted out.
Myself, I have no legal background, so I don’t know if these legal eagles are correct. Just an FYI on some of the legal thoughts out there.
Thanks!