The situation is growing more desperate by the hour in Venezuela as people dig through the rubble of collapsed homes and apartment buildings three days after twin earthquakes struck the country, leaving hundreds dead and thousands trapped. 

Venezuelans took the search for missing loved ones into their own hands, citing a scarcity of government rescuers, as the human toll of Wednesday's quakes climbed. Aid agencies consider the first 48 to 72 hours to be a crucial time frame to retrieve people alive, though that can be extended if they have access to food and water.

Venezuelans reported seeing few state rescue teams in the hardest-hit areas, despite authorities projecting an image of a robust government response. Acting President Delcy Rodríguez said the Venezuelan government was mounting a full response during these "critical hours for rescuing people alive" and welcomed the arrival of international rescuers and humanitarian aid. 

Diana Sandrano told "CBS Saturday Morning" her brother has been missing for two days. The building where he lived was destroyed in the quakes. Rescue workers and search dogs scoured the building as she prayed for a miracle. Sandrano said she will search for him "as long as it takes." 

"He deserves to live and have a future," Sandrano said, after a day of searching. 

More than 200 people have been rescued so far, the government of Caracas said. But about 51,000 remain missing. The figure likely includes people who have been unable to communicate with loved ones due to the lack of cellphone signals, and some reports may be duplicates. 

The International Organization for Migration said up to 6.76 million people in Venezuela could be affected by the earthquakes, including some 2 million in Caracas alone.  

Officials block access to epicenter as families wait and hope 

Authorities announced Friday night they would block access to La Guaira, the epicenter of the destruction just north of Caracas, as chaos and traffic began to hamper search efforts. Anyone who wants to enter would now have to seek official permits, but provided few details of who would be allowed in.

Rodríguez said food and water is being distributed in the region by government officials. She said La Guaira had been militarized and more help was on the way, even as residents said it was just a fraction of what they needed.

Nazareth Jimenez sobbed into a loved one's shoulder as she watched neighbors use hammers and power tools to try to cut through slabs of concrete in a building reduced to a mountain of debris. She was wracked with anxiety as she waited to see if her siblings, nephews, nieces and friends would emerge alive.

"My God, how are we going to get them out of there?" Jimenez said.

Jimenez pleaded for machinery capable of moving collapsed structures. 

"We're making a call for help to the government and countries across the world," she said. "There are still people alive in there."

Omar Reyes said around 20 family members died in the disaster. 

"I've been left alone in this life," Reyes said, walking through the rubble where two of his children were buried.

Because the two quakes took place within a minute, many people did not have time to evacuate their buildings, Northwestern University professor emeritus Emile Okal told CBS News. The shallow depth of the quakes led to a massive impact on the surface. 

The twin earthquakes were also followed by a series of aftershocks, including a 4.5-magnitude quake recorded on Friday. Loyce Pace, the International Red Cross' regional director for the Americas, said "people are still terrified to reenter what were their homes." 

Earthquakes amplify economic and political turmoil 

The disaster poses a huge challenge for Rodríguez, the former vice president who took office in January after the capture and removal of then-President Nicolás Maduro by the United States. Venezuela has been facing economic disarray for more than a decade, and many people reject the legitimacy of the political movement Rodríguez represents.

In the city of Maiquetia, people lined up outside stores and pharmacies that served them one by one behind closed doors. At one point a woman in a crowd threw herself to the ground to protect a package of diapers with her body, desperate to keep it.

Traffic and throngs of motorcyclists at times disrupted search efforts. Mexican soldiers and volunteers repeatedly asked for silence to try to hear signs of life under the rubble, but bikers — civilian and uniformed — continued to honk horns and rev engines. 

Some people began to carry off basic goods such as toilet paper and food from stores in Catia La Mar, a neighborhood in La Guaira that holds over 200 housing towers. Others swarmed a civilian pickup truck that was giving out bread and water, until a soldier intervened. The parking lot of a pharmacy turned into a makeshift shelter with tarps, hammocks and tents.

A few miles away, Yuleidy Cadenas, 28, stood across the street from a collapsed public housing building, hoping her son, mother and brother would be pulled out alive.

She fled barefoot from another building as it collapsed Wednesday and found her mother's 12-floor apartment tower had pancaked.

"I got on top of the rubble and told them to yell back, and nobody did, not my brother, nor my son or my mother," Cadenas said.

International rescuers bring resources and expertise 

Venezuelan authorities said Friday that 861 volunteers from Mexico, the U.S., El Salvador, Switzerland, Colombia and beyond were in the country, and more were coming from elsewhere.

Rodríguez said she spoke to President Donald Trump and Secretary of State Marco Rubio on Friday and they reaffirmed their commitment to send rescue teams and aid equipment. 

The U.S. resources included search and rescue teams from Fairfax County, Virginia, and Los Angeles, Rubio said Thursday. The U.S. has also sent medical resources and humanitarian aid, he said.