This is one of those things that drives me absolutely bonkers. Seriously. Whenever our public discourse turns to the question of a candidate's "character", we end up talking about something that "everyone" seems to understand without anyone actually sitting down and defining the term. I think George W. Bush actually "gets it" better than most, because whenever he has appointed someone to a senior position, his public statements usually include the phrase, "he is a good man", as if that trumped every conceivable argument. This is the character issue in a nutshell - if a person hugs his or her kids, walks the dog, and puts the clean laundry away without being reminded, hey, that's good enough for me.
The issue of "character" really came alive in the 1990's, when the Republicans, while reaping a certain electoral whirlwind, had difficulty dealing with the on-going popularity of Pres. Clinton. Since his policies were liked by most Americans, they decided to take him down on his personal foibles, either real or alleged. Now, one could argue that this begs certain questions of character - what kind of scruples does an individual or a group have that is willing to do anything, including lie, go after someone's family, etc., in order to achieve a political victory? - but that issue was never addressed. To this day, conservatives are convinced that Bill Clinton was not just a bad President, but a morally degenerate human being unwilling to sit in the Oval Office. Considering the absolute mess the current occupant has made of things, I think that even if every charge against Clinton were true, I would still prefer a scoundrel.
A person can be morally vicious in his or her private life, yet be extremely good at one's job, and be preferred to someone who is upright and true, yet demonstrably bad at the same job. Electing the President of the United States is hiring a person for a job. We don't list our character points on our c.v.'s for the very good reason - our potential employers do not care if we are "good people". They want to know if we can do the job we are hired to do. Period. That's all. We have been fortunate in this country that we have had examples of great politicians who have also been overflowing in personal moral integrity. Yet, one could also argue that our two greatest Presidents, George Washington and Abraham Lincoln, were also flawed in this regard (Washington was a bit of a moral scold, and thought a bit too much of his own ethical rectitude; Lincoln's marriage was a stormy affair, partly because both he and his wife, Mary Todd, were chronic depressives and had little emotional energy left to deal with each other's problems). Yet, for the most part, Presidents, whether great, good, or awful, are just people, with all the moral complexity and limitations that implies. Whether it is Warren Harding sitting in the White House getting drunk during prohibition; Richard Nixon railing against Jews to his Chief of Staff; or Franklin Roosevelt relaxing in Warm Springs, GA with his mistress - well, some character flaws are bigger and more relevant than others. In the end, though, even had Harding been a tea-totaler, it wouldn't have mattered because he had many other limitations as President. Ditto, Richard Nixon. Roosevelt's long-running affair, while a burden to his wife, didn't mean he couldn't perform the duties of the Office of President, anymore than his polio limited him, because he was a larger than life individual (rare, but they do come along). Teddy Roosevelt was a belligerent war-monger and imperialist who nonetheless managed to broker a peace between Russia and Japan and earn the Nobel Peace Prize.
In the end, character in politics doesn't mean all that much. It's actually sitting down and doing the job the counts.
