The 112th Congress will not begin today even though Clause 2 of the 20th Amendment states:
The Congress shall assemble at least once in every year, and such meeting shall begin at noon on the 3d day of January, unless they shall by law appoint a different day.
The 20th Amendment, which was ratified in January, 1933 changed the initial meeting day of a new Congress which had been, according to Article I, Section 4:
The Congress shall assemble at least once in every Year, and such Meeting shall be on the first Monday in December unless they shall by Law appoint a different Day.
Keep in mind that was the first Monday in December of the year following the elections. If the 20th Amendment had not been ratified, the Democrats would continue to control the House and Senate as a lame-duck 111th Congress until next December 5th.
The 20th Amendment also changed the date of the beginning of a Presidential term from March 4 to January 20.
Senators, remember, were not selected by election of the masses prior to the ratification of the 17th Amendment in 1913. According to Article I, Section 3:
The Senate of the United States shall be composed of two Senators from each State, chosen by the Legislature thereof.
In the 18th century, transportation and communications were such that it was often difficult to determine who had won which election. For the winners, getting their affairs in order and making the trip to Washington, DC (when it became the seat of government with the signing of the Residence Act in July of 1790) was often an arduous and time-consuming ordeal.
By the way, the Residence Act, which established what we now know as the District of Columbia, passed the House by a vote of 31-29 and the Senate by a vote of 14-12 and originally included land ceded by both Maryland and Virginia. The government didn't think it needed the Virginia piece so the land which now makes up Arlington County and Alexandria City was returned to the Commonwealth.
To show there is nothing new under the sun, the compromise which put the Capital in its current location had to do with resolving an argument between northern and southern states over paying off the debts which had been accrued during the Revolutionary War.