TIJUANA, Mexico -- After a month-long trek through Central America, nearly 200 migrants have set up an encampment in Tijuana, Mexico. They're waiting to ask for asylum despite U.S. Customs and Border Protection (CBP) announcing the San Ysidro port is at capacity.

Mirna Aldana's 1-year-old son and several other children are just recovering from fever and the flu after traveling through Mexico on a train called "The Beast."

She is seeking asylum after two of her family members were killed by a gang. She's part of an annual caravan that started in Chiapas, traveled up the Pacific Coast to Mexico City, through Sinaloa and eventually to Tijuana. She said they can't live there anymore.

Less than a two-hour drive away, Vice President Mike Pence talked about immigration enforcement on Monday.

"We've been watching with great interest the advance of the so-called 'caravan,'" Pence said.

Asylum seekers like Miriam are following U.S. law. They have to prove a credible fear of persecution in their home country.

If they pass that initial interview, they will likely have to make their case to a judge, who will decide whether to grant asylum. Last year, only four applications from this caravan were granted admission.

The group was largely ignored until Mr. Trump used them to highlight the immigration debate.

"Our immigration laws in this country are a total disaster. They are laughed at all over the world," Mr. Trump said.

"It became really public after Donald Trump kind of got angry at the caravan," said Irineo Mujica, director of Pueblo Sin Fronteras, the group that started the caravans back in 2008.

He said most people here have little choice but to wait.

"This is a temporary separation. If they go back to their countries the separation will be final because a lot of them will die," Mujica said.

A Mexican immigration official tells CBS News the standoff is causing bigger problems for the U.S. and Mexico.