Is early voting unconstitutional in Tennessee?

According to the office of Tennessee Secretary of State Tre Hargett, 530,522 Tennesseans have already cast their ballots in for this coming Thursday's State primaries via early voting. Last Wednesday I proposed that the next General Assembly should make it even easier to vote early by eliminating the wait between the end of the current early voting period and Election Day by allowing people to vote right up until Election Day, simply moving to voting in the precincts on Election Day itself. On my blog The World According To Oatney, a commenter Glen maintains that early voting is unconstitutional:
 

I still maintain that early voting is unconstitutional. The Tennessee Constitution names the days that specific elections are to occur (e.g. first Tuesday after the first Monday). For the life of me, I don't understand why this has never been challenged.

Glen may have a point per the Constitution of the State of Tennessee (1870), Article II, Section 7:
 

The first election for Senators and Representatives shall be held on the second Tuesday in November, one thousand eight hundred and seventy; and forever thereafter, elections for members of the General Assembly shall be held once in two years, on the first Tuesday after the first Monday in November. Said elections shall terminate the same day.

For those of us accustomed to early voting, that is stern and fixed language that would seem to prohibit the practice at least where the November General Election is concerned. There is not an out, such as sometimes occurs in other constitutions, with the phrase "unless the Legislature shall by law appoint a different day." The State Constitution does not allow for a different day or for the General Assembly to prescribe other voting arrangements without a constitutional amendment.

It could be argued that early voting in primaries and local election could be allowed since there is no discussion in the Tennessee Constitution of primary elections or local elections, which take place on the first Thursday in August and in which we have either already voted or will vote this coming Thursday. That is a fair legal argument, but if we are to consider original intent where the Tennessee Constitution is concerned, it should be remembered that the custom of having an election on the first Thursday in August goes back to the time of settlement of this territory, and that our current State Constitution, ratified in 1870, is nothing more than a slightly modified version of Tennessee's original Constitution of 1796. That document fixed the date of elections for the General Assembly on the first Thursday in August and declared that they would terminate at the end of the following day, and there was again no "notwithstanding" language allowing legislative flexibility.

At least one current member of the General Assembly has told The Examiner that they believe that early voting actually makes it more difficult for  an everyday citizen to run for office, since they have to raise and spend even more money. So why hasn't anyone challenged Tennessee's early voting law? Probably because no one wants to be seen to be restricting voters' ability to exercise the franchise. It really doesn't make a candidate or a public figure look good to say "we want to restrict voting rights".

If Tennessee wants to continue early voting, however, the right thing to do would be to amend the State Constitution to allow for early voting, not to conduct our elections in a way that is blatantly unconstitutional merely because it is popular and convenient.