President Trump is threatening to impose new sanctions on Venezuela if the government rewrites its constitution.
Critics say President Nicolas Maduro wants to tighten his grip on power and silence protesters amid an economic collapse. Sanctions could include a ban of imports of Venezuelan oil, which could mean.
Venezuela has yet to allow CBS News to enter the country.
The bridge that connects Venezuela and Cúcuta, Colombia, has always been a busy border crossing, but the number of Venezuelans walking into Colombia only increases as the violence and instability in their country intensifies, reports CBS News correspondent Manuel Bojorquez.
The luggage coming through makes the border look like an airport. Thousands of Venezuelans cross daily in search of food, medicine and work. Some return home -- but Marcos Gonzales says he can't.
His wife, Liliola Gonzales, and son are coming with him. "There's no medicine," she says. "He has autism too and needs medication."
On the other side of the border, protesters and Venezuelan armed forces clash almost daily. They are fighting over the socialist government's policies, which critics blame for the economic collapse.
President Maduro fired back at U.S. attempts to intervene Tuesday.
"Yes, it's Maduro's fault," says 17-year-old Rosa Gonzales, a Venezuelan who left her country to give birth in Colombia. "You just can't have a baby there now, you can't get medicine, the hospitals are contaminated."
She says she doesn't know if Venezuela will be able to recover from this.
Marcos Gonzales and his family hope the country will, and hate to leave home. Through tears, he said, "this is real life.
This week, Colombia's president traveled to Cuba, Venezuela's ally, hoping to find a diplomatic solution to the turmoil.
But neither side is backing down.
The opposition says it will start forming an "alternate government" Wednesday.