If you are flying DCA-DFW-HKG, I presume that you are flying AA. If so, AA recommends 90 minutes for domestic and 2 hours for international. Not sure where you found the 2-3 hour requirements. AA's recommendations are right on its website:

an arrival time at the airport of one hour and thirty minutes prior to departure when traveling within the United States. When traveling outside of the United States, we recommend two hours prior to departure.

The minimum check in for domestic is 45 minutes prior to scheduled departure (domestic) and 60 minutes (international) and you must be at your departure gate no later than 15 minutes prior to scheduled departure (domestic) and 30 minutes (international).

If you are not a regular international traveler, are checking bags and do not have pre-check, give yourself the 90 minutes at DCA. So long as your documents are in order, e.g. passport and visa (if you require one), those checks should add about 30 seconds to check-in (and they will be checked again at the gate at DFW). The longest lines will likely be at check-in and unless you are flying in a premium cabin or have status, checking bags can take time. Try to OLCI, but do not count on it because you may not be able to complete it without a document check.

There is all manner of debate about whether the deadlines for international or domestic apply for a domestic connection to international, but AA's differences are so minimal, that it is not worth the hassle of a difference.