I strongly disagree with your post/analysis.  As originally constructed by the Founders, the President was, along with the Judiciary, among the LEAST representative of the three branches of government.

The President of the United States is NOT directly elected by the people AT ALL - s/he is elected, as I am sure you know, by a College of Electors chosen at the direction of the State Legislatures.  In fact, there is NO requirement in the US Constitution that the State Legislatures need hold a PUBLIC election to choose those Electors AT ALL.

The Judiciary, of course, is completely appointed, by the non-directly elected President and subject to confirmation by, what was at the time, the NON-directly elected US Senate (Senators being appointed by elected State Legislatures).

Of the Legislative Branch (at the time of the writing of the Constitution) only 1/2 of that Branch was DIRECTLY elected by the PEOPLE - and that, of course, was the US House of Representatives.  

Your argument that the President is somehow "closest" to the people, and therefore the Presidential Veto somehow confers some kind of safeguarding of the people's will is simply not borne out by the facts of our Constitutional system.  Congress was ALWAYS intended by the Founders to be the branch of government "closest" to the people - and with the 17th Amendment (Direct Election of Senators) - this was made even moreso.

Marc