That's a bit of a 'how long is a piece of string?' question because it depends on how fast you drive, how often you stop, and for how long etc. You should allow five to seven days to make the journy with minimal stops - longer if you want to have a look around as you go.
Thats a good response, i would allow anything around 7 days. If your pushing it, maybe 5, thats little sleep and remember not to drink the night before. Comfortably, why not take about 10 days though, see some sights along the way :)
You can do it in a little over 3 days if you have 2 drivers. I know that sounds absurd but I have done it. My sister and I drove from San Francisco to New York in a few hours over 3 days. Another time we managed to drive from San Francisco to New York to Boston to Chicago and back to San Francisco in 10 days. It wasn't a lot of fun, but we had specific goals in mind; the number one being time frames. The person posting this question may just be arriving in New York and need to get to San Francisco as quickly as possible. 3 Days and a few hours if you're traveling in good weather and there is no major construction on the interstate system.