If you OLHI, I generally show up around 1h before takeoff. I've gone through with Nexus with less than 35 minutes to takeoff - cab to gate in less than 15 minutes most days, even if you're going to the little plane wing (F80-F99).

Time of day / day of week can affect this. With a 06:30 flight, you should be fine with less than an hour .. except maybe monday morning.