While we do see examples of people who break with family political traditions, I believe posts 2, 3, 4 are correct: People usually hold political values that reflect their socio-economic status. The fact that these views are usually consistent within families is not necessarily just due to the "discussions" that family partake in. I really think it's due more to where the various family members fit into society. In general, and there are plenty of exceptions to this statement, members of a particular family are in roughly the same socio-economic place. A well educated, financially self-sufficent family is more likey to be politically conservative than a poor family who depends on some sort of public assistance to survive.
I am an example of the other side of the coin. Most of my family was of one political persuasion, while I was of another, most of the time anyway. So there are no hard adn fast rules.
So yes, family does play a role, but don't overlook the context in which that family lives as being, possibly, the primary determinant of one's political outlook.
A person is generally going to agree with the family or go in exactly the opposite direction when it comes to politics. Like religion, politics creates strong feelings in people. Yet also like religion, people are socialized to certain political views.
Families have many, many discussions. Many of these discussions directly and indirectly concern political values. Though we grow up talking with friends and classmates, we end up spending more time with our parents and siblings (if we live with them). This makes the home a natural place for political socialization to occur, especially as parents represent the primary socializing force in a child's experience.
Family members teach you what sorts of political values your family believes in. They tend to tell you what party your family supports. Even if they do not explicitly try to socialize you, you hear them talking about various political issues and you come to know what opinions members of your family are expected to hold.