The 20th Amendment sets the date of the presidential inauguration at January 20. That date can only be altered via constitutional amendment.
The trick is who is inaugurated on January 20. It could be the Speaker of the House inaugurated as Acting President if things aren't settled by January 20. Or if the election goes into the House and Senate, should the House be deadlocked and the Senate able to choose a Vice President, the Vice President would be inaugurated on January 20 as Acting President. The Acting President would hold office until things were settled and an actual President elected. Then we would have a second inauguration.
But on January 20, somebody will be inaugurated either as President or Acting President.
The Constitution orders other things that don’t happen as written.
When was the last time the House presented an annual budget each year as ordered under the Constitution?
correct there is provision for speaker