A man with well developed EMOTIONAL INTELLIGENCE can be able handle alot and keep things balanced for himself and his family.
Op I disagree with that as being said. There's no quality a man will have that he could be able to maintain a healthy long lasting marriage if he gets to be that man that is married to a cantankerous woman (a badly behaved woman). For God's sake the man is a human being too not a perfect machine and as such would need a good input from the woman's side to make the marriage go smoothly.
That's why it's called marriage because it's two people that's involved and needs not to be one person exerting efforts to making it work. There's no level of emotional intelligence you want to possess that you can't reach your limit of giving up if you're married to a uncaring woman that makes life rather difficult for you.
In a nutshell, a good healthy family is built with the effort of both partners not one sided.