My sister was born the day JFK was elected, Tues 11/08. This means that there was a Tues., 11/01. So, why wasn’t that Election Day instead? Some say it is the 2nd Tues of the month, but consider this year when Election Day is Tues., 11/02, and not Tues., 11/09. My wife thinks it must be the first Tues after the first Mon of the month. Is this correct? And/or, has it changed since JFK’s days? 
7 Nov 61 was a Tuesday/ (unless that calendar is wrong), and is also the first Tuesday in November.
The purpose of setting Election Day as the first Tuesday after the first Monday in November is so that Election Day does not fall on the first day of the month, or on the first day of the business week (Monday). Much business activity falls on those days, which would make it difficult to get to the polls.
Kennedy was elected in the 1960 general election, Brutus.
The reason for the “first Tuesday after the first Monday in November” law is to cause the date to fall during the first week in November, but not on November 1, which is All Saints Day, a significant religious holiday for many Christian denominations (especially several of those common in the early days of the country), and in particular a Holy Day of Obligation for Roman Catholics. The idea was that one could not easily attend religious observances at one’s home church and travel the distance to the nearest polling place in days gone by when modes of transport were less rapid than today, and the custom has been preserved because it maintains the SOCAS distinction by not having election day on a religious holy day.
Either that is what they want you to think, or I terribly misread the OP. You pick!
The First Tuesday after first Monday date was set back in 1845.
Well, since the OP didn’t mention a year, I’d say you not only misread it but injected into something that wasn’t there. And since there are no national elections in odd-numbered years like 1961, what were you thinking about?
Congress once passed a law requiring at least 34 days (but not more than, say, 39 or so) between the general election and the day on which the electoral vote would be calculated in each state capital; at that time four or five weeks’ time was necessary for returns to get to the state capitals from outlying county seats (counties were not divided into precincts yet). They figured that the earlier in the week the better, avoiding Sunday, of course; and they made Tuesday election day so voters wouldn’t have to start out traveling on Sunday, as would be necessary if Mionday were the day chosen.
They did not choose the first Monday, which, as noted, would be inconvenient for businesses doing bookeeping; also for courts’ calendars, apparently. They did not choose the second Tuesday, either, since that could fall as late as November 14, which would not allow enough time before the first Monday after the first Wednesday (per the statute passed by Congress) for all the electors to get to the state capitals and perform their duty. Therefore the first Tuesday after the first Monday was chosen; this would never be earlier than Nov. 2 or later than Nov. 8, allowing enough travel time for the electors.