I don't think DCA has ever closed due to capacity. From what I hear, Xmas eve crowds are much lighter than Xmas day. Either way, you'll know fairly early in the day (by 10/11 am) if they are expecting it to reach capacity. It happens in steps. Look for signs that say "EVERYONE needs a hand stamp for reentry" (even APs).
1. They only sell passes to DCA (not DL).
2. Only allow re-admits in, no new entries (new entries, even APs, directed to DCA).
3. Gates are shut to everyone, until they have enough people leave the park (usually after parades or fireworks).