A woman with stroke symptoms in Midwood, Brooklyn, waited for an ambulance for six hours, finally arriving at the hospital with telltale signs of advanced brain damage. In Forest Hills, Queens, bystanders waited for three hours next to a man lying unconscious in the snow before they were able to flag down help. And in Crown Heights, Brooklyn, a mother in labor who started calling 911 at 8:30 a.m. on Monday did not get an ambulance until 6 p.m., too late to save the baby.

As a blizzard bore down on New York City on Sunday and Monday, 911 dispatchers fielded tens of thousands of calls, trying to triage them by level of severity, from snowed-in cars at the low end to life-threatening emergencies at the highest. But even the ambulances assigned the most serious of the calls sometimes could not get there. At least 200 ambulances got stuck on unplowed streets or were blocked in by abandoned cars, city officials said Tuesday.

As the backlog of calls grew — it ultimately reached 1,300 at its highest point — an unusual directive went out across the computer screens within ambulances, emergency workers said. It told them that after 20 minutes of life-saving effort on a nonresponsive patient, they should call a supervising doctor, who would make the call about whether to give up. While it is rare for a person to be revived after 20 minutes, it is usually up to the medical crew to decide when to call the doctor.

Mayor Michael R. Bloomberg defended the city’s response to the storm on Tuesday, and called the digging out of ambulances the city’s first priority. He said nearly 170 stranded ambulances had been dug out by emergency crews, with 40 more still stuck Tuesday morning. Still, the impassibility of many streets made routine ambulance runs into odysseys, sometimes with life-threatening or fatal consequences.