I posted something last month, but haven't a clue where. Yes, T3 is a nightmare, particularly in the mornings as there are more than a dozen flights leaving within the first hour, and a second wave of a dozen up to 8am. Fortunately, US has only two flights before 7am, so the problem will not be the actual check-in, but the line into INS which is fed by all the other carriers.

The terminal has a single entry point from five US carriers, and two Canadian. Even having elite status just gets you into the main INS line a bit faster. I would check to see when US opens its check-in, but with a 6:15am flight, their check-in lines will likely start by 4:45/5am, with INS lines building once all the airlines open their check-ins too. The only positive is many of the jets out in this first wave are ERJs and CRJs, so less than 100 people per flight.

I had a 7:55am flight and arrived at 6:15am to huge lines in front of all the check-ins, and another hour to get through INS. [Bring a newspaper to read, the INS and Security lines move slowly.]

After INS, count on another 20 to 30 minutes to get through Security.

From the November OAG, here are the earliest flights out:

DL to Cincinatti at 6:00
DL to Atlanta at 6:35

AA to Boston at 6:25
AA to Chicago at 6:30
AA to Minneapolis at 6:30
AA to LGA at 6:30
AA to Miami at 6:55

US to Pittsburg at 6:15
US to DCA at 6:15
US to Philladelphia at 7:05
US to Charlotte at 7:15

CO to Houston at 6:15
CO to Newark at 6:29
CO to Houston at 7:10
CO to Cleveland at 7:15

NW to Detroit at 6:30
NW to Memphis at 7:10

SG to Newark at 6:35

Our prayers are with you...