Too soon?

I had a phone interview last Tuesday (10/23), and an in person interview last Thursday (10/25). Then they set up a second in person interview on Monday (10/29). All of the interviews seemed to go really well. At the last one, the interviewer said I asked a question that stumped her and she seemed to be impressed. They said they wanted someone to get started this week, so I’m kinda freaking out because I haven’t heard from them and I REALLY need this job. Is it too soon to follow up?