Yes, that is what it was called — not sure if that was the official name. I think it was halted because it did adversely affect citizens and we still had the Bracero Program, some of them may have been affected too. Personally, I do not recall news items at that time.
From wiki FWIW:
“Operation Wetback in action
The effort began in California and Arizona in 1954 and coordinated 1075 Border Patrol agents, along with state and local police agencies. Tactics employed included going house to house in Mexican-American neighborhoods and citizenship checks during standard traffic stops.
Some 750 agents targeted agricultural areas with a goal of 1,000 apprehensions per day. By the end of July, over 50,000 illegal aliens were caught in the two states. An estimated 488,000 illegal aliens are believed to have left voluntarily, for fear of being apprehended. By September, 80,000 had been taken into custody in Texas, and the INS estimated that 500,000 to 700,000 had left Texas of their own accord. To discourage illicit re-entry, buses and trains took many deportees deep within Mexican territory before releasing them.
Tens of thousands more were deported by two chartered ships: the Emancipation and the Mercurio. The ships ferried them from Port Isabel, Texas, to Veracruz, Mexico, more than 500 miles to the south. Some were taken as far as 1000 miles. Deportation by sea was ended after seven deportees jumped overboard from the Mercurio and drowned, provoking a mutiny that led to a public outcry in Mexico.