Colapsar/saturar las líneas telefónicas.

To jam phone lines/networks, to jam up phone lines, become clogged.

In News:

"A rare East Coast earthquake that shook people from North Carolina to Boston today prompted heavy call volume that jammed cell phone networks throughout the region."

CNet News.

"Before the earth had even stopped shaking Tuesday afternoon, thousands along the East Coast calling and texting loved ones jammed up phone lines across the country."
The Times.

"And as phone lines became clogged, social media websites like Twitter and Facebook became a place to communicate."
The Times.

"The high volume jammed up lines, but Schweder said the company has protocols in place to reroute calls and help ease the congestion."
NBC.

Foto: The Times (UK)