It's ideal for one parent to stay home and one parent to work. But the gender of the parents doesn't matter. A father can be just as good of a stay-at-home parent as a mother, and a mother can be just as much of a great breadwinner as the father. It depends on the circumstances.
The only thing women making more money than the man in their household could hurt is the male ego. Men who have traditionally used their "breadwinner" status to leverage against bearing their fair share of childrearing and home maintenance are now finding they are expected to properly pull their weight.
A man who has to base his self worth on making more money than his wife is no kind of man anyway.
First of all, what is the 'American' family? The heterosexual patriarchal nuclear family of the 1950s? There is no singular 'American family' anymore.
In any case, there is absolutely no way financial independence and professional success for women can hurt a family unit. How would it? Such a thing can only stand to increase the self-esteem and self-worth of the women in said units, making them more secure in their duties both inside and outside of the home.
Rather, I believe it is men, who feel threatened and emasculated, who refuse to share half of the duties at home, that are the real cause of any 'problems' in the 'American family' that may come with a rise in female independence.
It was historically acceptable for men, as breadwinners, to spend a majority of their time outside the home. But now that women are striving to do so as well, we are worried about 'problems' within the 'American family?'
Rather than an issue of gender, however, this is an issue with the entire societal structure that demands productive citizens spend more of their waking hours at work than at home with their families. How can ANY family unit be successful when they spend roughly 3 hours a day together?
We are much better off with strong independent women in the workforce. Being a house wife is ultimate degrading and demeaning and we never return to those dark days. We are moving above and beyond the sick oppression of the 1950's ideal of a broken nuclear family. This is a step in the right direction.