Inaugurations used to be held on March 4. This was the date used until 1934. As Garrett Epps points out in the January/February 2009 Atlantic:
This long delay nearly destroyed the nation after the 1860 election. During the disastrous “secession winter,” Abraham Lincoln waited in Illinois while his feckless predecessor, James Buchanan, permitted secessionists to seize federal arsenals and forts. By March 1861, when Lincoln took office, the Civil War was nearly lost, though officially it had not even begun.
In 1932, Franklin Roosevelt crushed the incumbent, Herbert Hoover, but had to wait four months to take office. During that period, Hoover attempted to force the president-elect to abandon his proposals for economic reform. Roosevelt refused to commit himself, but the resulting uncertainty led the financial system to the brink of collapse.”
Obviously the long interregnum was not working out. The Twentieth Amendment, passed in 1933, cut the waiting period nearly in half. As the website infoplease explains:
The Twentieth Amendment, sometimes called the Lame Duck Amendment, was introduced to amend the Twelfth Amendment and shorten the time an outgoing President and member of Congress could be a “lame duck” -that is, a public official who continues to serve after an election and before a successor’s assumption of office. The Twentieth Amendment moved the President’s start date up to January 20 – two weeks after the Electoral College’s votes are certified by the president of the Senate.”
Assuming there is ever any question that must be resolved by a vote certification, this gives the winning candidate a short, but decent, time to prepare.