Submitted forms and had interview. The guy was super friendly but said the emergency passport probably wouldn't be ready until tomorrow morning.
There were two factors that seemed to slow things down: (1) due to a weather advisory, workers in DC were told not to commute in during the morning which reduced embassy staff; (2) there were some oddities with the verification of the birth certificate.
Besides when the emergency passport could get done by, the other big question that emerged was whether to apply for the full replacement passport in DC and have it sent to Vienna or just apply in Vienna.