Often times, when a political candidate refers to history, they warp it tremendously into propaganda to push their points, but what they said has a nugget of truth to it to some degree (with the notable exception of /r/badhistory favorite Ben Carson). Last night in the Republican Debate, Donald Trump said that Eisenhower repeatedly moved immigrants just south of the border, which failed, and then he moved a million illegal immigrants much further south and it was a success. I assume he's talking about Operation Wetback.
It's hard to address something this big in a single post. Migrations are a complicated subject, especially for 20th century Mexicans. After the diaspora of the revolution, many Mexicans in the borderlands had established transborder identities and social networks. It's important to remember that the border of the early to mid 20th century was delineated primarily by its remoteness rather than the political lines. Mexicans would migrate to the border towns and simply cross. When immigration was being enforced, they would make use of their networks to evade political authorities.
It's important to note that the Mexican government itself considered this a problem, having written regulations on legal emigration into the 1917 constitution. Fast forwarding a few years to the early 1940s, US agribusiness was expanding at phenomenal rates and the internment of Japanese-Americans during WWII led to a severe shortage of labor. Lawmakers instituted the bracero program to meet labor shortfalls with Mexican labor. Eligibility for the program required letters from local officials and to be in general good health, conditions many of the poor of Mexico were unable to meet. When these Mexicans were turned away at the border, they took to crossing by rather less legal methods to support themselves and their families.
The labor drain caused by this illicit migration had severe effects on northern Mexican agribusiness and revitalization projects. Political and agricultural leaders in Mexico began to demand that the US police its border more effectively to keep laborers from crossing. The US responded to these complaints with the hiring of an additional 150 inspectors, bringing it almost up to par with the manpower deployed to Canada's border. This had very little effect and by the end of 1943 Mexico threatened to shut down the Bracero Program if action wasn't taken. This time the Border Patrol responded more effectively, forming a number of deportation teams tasked with rounding up illegal immigrants in Chicago and Texas. These early deportees were taken to Nogales, AZ and El Paso, Tx and forced to cross. Undeterred, many simply came back a few days later.
Mexico agreed to transport captured deportees from the border to the interior in January of 1945. Upwards of a thousand immigrants a week were taken by train from Nogales and El Paso to Monterrey and Torreón. By the early 1950s this policy also included airplanes until funding was interrupted by Congress in 1953.
Treatment of those deported ran somewhere between bad and criminal. Mexicans were given little choice in where they were deported to, being guilty of illegal emigration. On the US side, chronic offenders at one Border station in Mission, Texas had their heads shaven, beaten, and humiliated. When outcry began against this practice, the Border Patrol ordered it stopped. The practice became official policy 7 years later for hygienic purposes.
After the construction of the fence started in the mid 1940s and with apprehension rate climbing, migrants were forced out into the desert to cross, with bodies being found daily. Throughout all of this migration continued to increase while apprehensions climbed even faster.
The reality is that it's a very complex period of intense collaboration between the US and Mexican governments to solve what became known as the Wetback Problem. Cooperative police and military action combined with coordinated legislative agendas formed the underpinning of the migrations and deportations. But individual needs and opportunities created vast economic incentives for many to risk the migration. Although removing deportees from the border had some effect, it failed to address the underlying context that was responsible for the migration.
An excellent summary of much of the literature, some of the problems in the deportations, as well as social and political context of the transborder region during the period can be found in:
Hernández, K. L. (2006). The crimes and consequences of illegal immigration: A cross-border examination of Operation Wetback, 1943 to 1954. The Western Historical Quarterly, 421-444.
As a follow up, did this act lead to any beneficial outcome for the US?