My question here is, "How has the enforcement (and attitude) toward the USA-Mexico border changed over time?
The US has a long history of strained border relations with Mexico, especially early in Mexico's history. New Spain, which later became Mexico, was often a place where slaves would flee their masters. Texas declared independence from Mexico in 1821 and a war was fought. Mexico abolished slavery in 1829 causing more slaves in the US to flee there and increasing tensions. Read more here. Mexico refused to accept the new borders for Texas, which led to Mexican-American War from 1846-1848.
The US gained large amounts territories once owned by Mexico. slavery was abolished shortly afterward in the US in the American Civil War. From reading various material from that time, attitudes changed more towards concerns of integrating the new Mexican citizens into American society instead of enforcing borders or preventing a flow of American or Mexican citizens across the border. Perhaps, there was concern of preventing Native Americans from crossing the border freely at this time, since the the US army was trying to keep them on reservations, which was not always successful.
In the 20th century, concerns shifted towards migrant Mexican labor in the Great Depression. Efforts were made to restrict the number of these laborers by requiring employers to have work visas for them. Many Mexicans were deported during the Great Depression as well. Quotas for workers and deportations were used again in the 1940s-1964's when economic conditions worsened after WWII, under the "Bracero Program." and "Operation Wetback."
"The Immigration and Nationality Act of 1965, also known as the Hart-Cellar Act, abolished the system of national-origin quotas. By equalizing immigration policies, the act resulted in new immigration from non-European nations..." Wikipedia. The US has used broadly similar immigration enforcement since this time, but there are many that would like to change it for many reasons, such as international terrorism or drug cartel violence which this answer doesn't address. Thus it is in the news.