“I believe that those electors are obligated to vote only for candidates who are eligible - 35 years old, natural born citizens, resident for 14 years. I think that they are obligated to consider qualifications. And, I assume that they always have.”
You assume completely wrong. There are many possible examples where Electors have voted for ineligible candidates, including Obama and McCain. However, there is one such example that is indisputable. In the General Election of 1872 the Liberal Republican candidate, Horace Greeley, earned 66 Electoral votes in the popular election. Unfortunately, he died on November 29th, before the Electoral College cast their votes. Consequently, his 66 electoral votes were redistributed to the other candidates, except when three Electors chose to vote for Horace Greeley in the Electoral College despite his prior death. Now, a candidate cannot be anymore ineligible than by being dead, yet three Electors went ahead and cast their three votes for a dead and therefore ineligible candidate. Congress subsequently invalidated those three electoral votes for the dead and ineligible candidate, Horace Greeley. If Congress had seen fit to disregard the ineligibility of the dead candidate, however, there would have been nothing to prevent those three electoral votes for a dead and ineligible candidate from being recorded and taking effect as it has for later ineligible candidates such as McCain and Obama.
In any event, our system has worked well for over 50 straight elections. Obviously, they have sometimes chosen people that we might not have chosen, but the system isn't designed to make all of us happy all the time. The fact that we don't like a particular candidate does not mean that we should try to concoct a crackpot theory based upon invented facts so that we can pretend that we have been victimized by the system.
In my view, a citizen at birth is a natural born citizen and that definition even applies to the candidates that I don't like for other reasons.