I don't know about American, but on Alaska/Horizon, I believe it is 4 hours before flight time.
Last year, I was doing a segment run to take advantage of the AS/AA promotion. I had scheduled PDX-SEA-PDX-SJC, and on check-in at PDX, I asked if I could just check my luggage for the final PDX-SJC segment. The agent looked at the schedule and allowed it because that segment was less than 4 hours away.
And afang, in case you weren't aware, at almost all hotels you can ask the bell captain to store your luggage for you until you're ready leave. I've often had situations where I check out in the morning, store my baggage at the hotel while I'm at my business meeting, then collect it when I'm ready to head to the airport. No charge, as such, but I always give a tip.