Question

If the house fails to elect a president by january 20 the 20th amendment says that

Answer 1

The answer to the question above is the Vice President shall act as the President of the United States.
If the House fails to elect a president by January 20th, the 20th Amendment says that the Vice President shall act as the President of the United States. It is on the Section 3 of the 20th Amendment.

Answer 2

The vice-president elect becomes the acting president until a new president is elected. The 20th amendment has several sections detailing the the dates and times for remaining in power for the president and other members of government. The end of the President's four year term is marked on January 20th at noon, when they stop being president.