As with most traffic issues, there is no definitive response. In general, on your commute either way you will encounter tight pockets of traffic but it should be moving. (The closer to 5:45AM you leave the airport the better - the closer to 6:30AM, obviously, the greater the volume of traffic - same to be said on your outbound commute). You should be able to make it in in about 30 - 40 minutes.
I generally take the el (Blue Line) to the airport from downtown - it takes about 45 minutes. I am also a cheap traveler - the el is about $1.50 versus $30 to $35 for a one way taxi ride.