They could! But it would take amending the Constitution to do so and that requires a 2/3 vote in each chamber of Congress and ratification by ¾ of the states: a long and involved process.

The 20th Amendment to the Constitution states "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 3rd day of January . . . and the terms of their successors shall then begin." It was ratified in 1933; took effect in 1937, and we've all been standing out in the cold ever since! Ironically, our first President's inauguration was held in your preferred month – on April 30, 1789.

After that first inauguration, the effective date for a new President's inauguration became March 4, and stayed there until 1937. When the March 4 date was enacted by Congress in 1792, an interval between the date of an election and commencement of office made sense. Without modern means of communication and transportation, it took time for the results of elections to be known and for public officials to make the sometimes long trek to the capital city from remote areas. Many of our early leaders were gentlemen farmers. The winter months inbetween the election and the start of a new government also was the interval between the harvesting of crops and the planting of new ones, when they could afford to take the time to turn to affairs of state.

The 20th Amendment shortened the interval between a November election and the time a president's term ended in March. By moving the end date from March 4 to January 20 [and in the case of Congress, January 3rd,] proponents of the 20th Amendment hoped to put an end to the "lame duck" syndrome. The 20th Amendment is often called the "Lame Duck" Amendment.

Officials on their way out were often referred to as "lame ducks," because they were perceived to be able to accomplish little of value during the time after the election and the end of their term in office. In effect, their authority had been "crippled," either by the voters, or the approaching end of their natural term. Congress was less likely to support an out-going president's initiatives, and a returning president was less likely to sign off on laws sent him by a Congress whose majority may have shifted. There was also concern that defeated incumbents might engage in foolish actions before leaving office.

The briefer interval established by the 20th Amendment was also a compromise between the desire to reduce the length of the awkward state of seeming to have two presidents – the out-going one still in office and the incoming president-elect -- yet still allow time for an orderly transition period between administrations.

The reason for having an interval between the new Congress convening on January 3 and the new President taking office on January 20 may have been to allow the outgoing President some time to consider the outgoing Congress' legislation for signature or veto. According to the Senate Historian's office, back when both the President's term and the Congress expired on the same day, March 4, it was not uncommon for the departing President to spend his last nights having to sift through last-minute legislation.