There should be people somewhere in between where the plane lands and where you head into the customs hall that will be looking for travellers with tight connections (I also fly to DC from Europe). The red card gets you a bit of help at passport control/customs (if you do not have GE) and again upstairs at the TSA check (if you do not have pre-check).

My one word of advice is to go up the escalators after you exit the customs hall and to skip the elevator, which can be quite slow.