Beyond "nurturant parent"
Lakoff's strict father/nurturant parent distinction is widely misunderstood. Some people are unclear on what nuturant parenthood entails. They incorrectly assume that "nurturant" is a euphemism for weakness or effeminacy. Cortunix dispels many of those misconceptions here.
More often Lakoff is criticized for his choice of labels. We know that it takes courage, strength, and resolve to be a nurturant parent--but those aren't the associations the term evokes in most people.
I think this is Ezra's worry:
So the strict father frame the Republicans use immediately paints Democrats as mommy. And while mom is awesome, it's dad you call when you hear noises downstairs late at night. That's how Republicans win elections, they basically mount the stage and say "did you hear that, America? I think I heard someone jiggling the door downstairs! Now would you rather have George Bush and his bat go check it out, or should we send John Kerry and his baguette?" So Lakoff responds to this by suggesting that Democrats become a gender neutral nurturing parent, which simply doesn't exist, and would actually just mean mom.
It's important to note that Lakoff doesn't recommend that progressives explicitly evoke the nurturant parent model in their daily rhetoric. It's more of a tool to figure out where other people are coming from.
Lakoff argues that all of our reasoning is influenced by metaphors. Metaphors relate abstract or unfamiliar concepts to ideas we already understand. For obvious cultural and biological reasons, "family" is a powerful metaphor for many different human affiliations. So it's not surprising that nations, churches, armies, corporations, and organized crime syndicates have evoked the family in their rhetoric for centuries. (Founding fathers, sons of the revolution, Holy Fathers, brothers in arms, the XYZ family of companies, godfathers....)
Everyone likes families--but liberal and conservative world views prescribe different ideals family life. So, the Lakoffian question is this: If the nation is like a family, what kind of family should it be? For conservatives, the ideal family is an authoritarian hierarchy ruled by a strict father. Liberals idealize a nurturing family that encourages each individual to achieve her full potential. It's important to note that both sets of metaphors resonate with everyone to some degree.
I think it would be better for liberals to think of the Nurturant Family as the counterpart to the Patriarchal Family. Note that "family" is a metaphor for our ties to our fellow citizens, not just a metaphor for the relationship between the government and the the people. If you think that families and countries need strict fathers, it makes sense to make the President the strict father of the country. But if your ideal society is like a nurturant family, it would be paradoxical to elect one uber-nurturer to succor us all.
The ideal liberal family is a multi-generational collaboration. Power is shared among family members. In the idealized liberal family mothers and fathers collaborate to raise their children. Parents have an important role, but so do aunts, uncles, grandparents, and of course, brothers and sisters. It's no accident that feminists, trade unionists, minority leaders, and other progressive groups use sibling metaphors to express their ties to their allies. You can count on your brothers and sisters to watch out for you.
Hilary Clinton infuriated the wingnuts with her remark that "it takes a village raise a child." Metaphorically, her comment was a direct attack on the strict father model.