Who knows?
If Dem Supporters + Mail Fraud v. Trump Supporters turns into a Hayes v. Tilden, Bush v. Gore, endless election scenario and the election is deemed indeterminate, then Pelosi (assuming something happens regarding her fight for a new term) probably takes the office.
She doesn't.
I've seen outlets like CNN try to push that idea, but
3 U.S. Code § 19 doesn't come into effect if the election results are delayed so long than neither Trump nor Biden are declared the winner by Jan. 20th.
(1) If, by reason of death, resignation, removal from office, inability, or failure to qualify, there is neither a President nor Vice President to discharge the powers and duties of the office of President, then the Speaker of the House of Representatives shall, upon his resignation as Speaker and as Representative in Congress, act as President.
3 U.S. Code § 19 has nothing to do with a sitting President. It doesn't cover delayed election results, and in the case of a Constitutional order of succession
and the contingent elections by the House and the Senate, those are also not covered by delayed election results. Contingent elections happen
after the votes are already counted. The House elects the president and Senate elects the vice president. The House and Senate will need representatives of two-thirds of the states present, and again, this doesn't apply for delayed elections, it's a completely unrelated scenario.
The only Constitutional and legal answer to what would happen if the election was delayed beyond Jan. 20th is that someone in Trump's cabinet would be appointed as acting President until the votes were finished being tallied. In the extremely unlikely event that this happened, what you'd probably see is President Pompeo.
The entire thing is just wishful thinking. There are
dozens of people in Nancy's way before she could use 3 U.S. Code § 19 to assume the presidency in this scenario. The media is just abysmal at fact-checking when it comes to situations that they can use to slavishly pen up fan-fiction for It's Her Turn.