The following is a likely timeline of government's response. Assuming the city in question is moderately sized (under 100,000 population), without a busy commercial airport or industrial facilities that may be a cause of a significant accident. The city is located in American backcountry, with a number of smaller towns around, but no significant metropolis nearby. Falling unconscious is a momentary event, which has happened during the day. Everyone crossing into the city after that moment keep consciousness without problem.
1st minute: Cars driving in the city and out of it lose control. People on the phone stop responding. First fatalities. People driving into the city observe car accidents, people on the line start worrying about their relatives.
2nd minute: People who just arrived in the city and those on the line try to contact others in the city, 911 line or other emergency services. There's no response. More people are crossing into the city by car.
5th minute: Law enforcement and emergency services outside the city are notified about the situation. While the scale of the event is not clear yet, first responders are being dispatched.
10th minute: First responders are reaching the city. Wider range of authorities are notified. In the meantime, people staying in hospitals or injured in accidents are dying.
30th minute: All news outlets are notified of the situation. People are livestreaming from the "ghost city". President is notified as well. Massive help is being dispatched.
1st hour: Emergency responders are taking situation under control. The city is cordoned off. Unconscious people are being transported to hospitals, just in case.
2nd hour: Army units are engaged and taking over control. Investigative teams are trying to do their best.
4th hour: All unconscious people are either transported to hospitals or otherwise placed under supervision.
47th hour: City is cordoned off, situation is fully under control, but no one has a clue about the situation. News outlets all around the world are covering the situation.
48th hour: Everyone wakes up, and no one still has a clue.