SAN CRISTÓBAL, Venezuela — One moment, the Casique family was piled on a motorcycle, on the way to school: the mother, a son and Nora, the 8-year-old daughter. A fraction of a second later, a truck had barreled into them.

The accident landed the family in the hospital — and condemned the father, Israel Casique, to scour pharmacies and the black market, or travel to Colombia, in an endless search for the medications and supplies they need to survive in a country where the health care system is in collapse and hospitals lack even basics like soap and alcohol.

The arrival of American donations of food and medical supplies to the Colombian border with Venezuela appeared to be a lifeline for the family and dozens of other patients in critical condition or with serious chronic diseases interviewed by The New York Times last week.

But the delivery of aid has become the epicenter of an escalating political confrontation between President Nicolás Maduro of Venezuela and the country’s opposition, and the impasse has kept the supplies stuck in a converted customs warehouse in the Colombian border town of Cúcuta — and out of Venezuela — for nearly two weeks.