By federal law since 1792, the U.S. Congress permitted the states to conduct their presidential elections (or otherwise to choose their Electors) any time in a 34-day period before the first Wednesday of December, which was the day set for the meeting of the Electors of the U.S. president and vice-president (the Electoral College), in their respective states. An election date in November was seen as useful because the harvest would have been completed (important in an agrarian society) and the winter storms would not yet have begun in earnest (a plus in the days before paved roads and snowplows). However, the problems borne of this arrangement were obvious and were intensified by improved communications via train and telegraph: the states that voted later could swell, diminish, or be influenced by a candidate's victories in the states that voted earlier. In close elections, the states that voted last might well determine the outcome.
A uniform date for choosing presidential Electors was instituted by the Congress in 1845. The actual reasons, as shown in records of Congressional debate on the bill in December 1844, were fairly prosaic. The bill initially set the national day for choosing presidential Electors on "the first Tuesday in November," in years divisible by four (1848, 1852, etc.). But it was pointed out that in some years the period between the first Tuesday in November and the first Wednesday in December (when the Electoral College met) would be more than 34 days, in violation of the existing Electoral College law. So, the bill was amended to move the national date for choosing presidential Electors forward to the first Tuesday after the first Monday in November, a date scheme already used in the state of New York. Many theories have been advanced as to why the Congress settled on the first Tuesday after the first Monday in November.
As for the day of the week chosen, in 1845, the United States was an agrarian society. Most people traveled by horse and buggy. Farmers needed a day to get to the county seat, a day to vote, and a day to get back, without interfering with the Sabbath. So that left Tuesday and Wednesday, but Wednesday was market day. So, Tuesday it was.
I think as some point, we'll have to concede that 1 day is simply not enough for 300 million people to vote. I hope that day isn't November 5th 2008.