The 20th Amendment (article 1) of the US Constitution states that
The terms of the President and Vice President shall end at noon on the 20th day of January, and the terms of Senators and Representatives at noon on the 3d day of January, of the years in which such terms would have ended if this article had not been ratified; and the terms of their successors shall then begin.
However, the time itself is not a fixed notion. Twice a year it suffers from gaps/overlaps when we change to/from the Daylight Saving Time. So, presume a hypothetical situation where a President announces the new "president saving time" such that on the 20th of January at 11am the clock moves forward by 2 hours. Thus, the next moment after 10:59:59am is 1:00:00pm. The noon does not occur on that particular day. Correspondingly, he claims, his presidency failed to end according to the 20th Amendment, and in fact can now continue forever.
A slightly less extreme version could be to move the time backwards on the same day: from 1pm to 11am. Then the noon would occur twice, forcing the incoming president's term to end almost immediately after it began.
Is such action even possible (presuming the President does not care about any public outrage/political fallout)? What mechanisms exist to protect against such abuse?