The Post corrected "5 myths about immigration" in the Outlook section today. The first of the myths is that "immigrants take jobs from American workers." It dismissed this concern by telling us that: "economists also estimate that for each job an immigrant fills, an additional job is created." It might have been helpful it had included some names here of economists who hold this view. There are certainly some economists, such as Harvard Professor George Borjas, who see immigrant workers as having a substantial downward impact on the wages of less educated workers.
There also is an important question about who gets counted as an "American worker" in this story. Some analyses have concluded that immigrant workers have little impact on the wages of native born workers, however they do have a substantial negative impact on the wages of other immigrants. Of course many immigrants will become American citizens after being in the country for 10-15 years. So, if we count naturalized citizens as "American workers" then the Post's assertion is completely untrue.
It is worth noting that recent immigrants have had a much more difficult time in catching up with the wages of their native born counterparts than was true in 60s and 70s. This can be partially explained by the larger flow of immigrants in the last two decades.
It is also worth noting that there may be a difference between the marginal impact of more immigrants and the impact of a larger flow over time. In industries like residential construction and meatpacking, native workers have been largely displaced by immigrants over the last three decades. These industries had provided relatively well-paying jobs to workers with little education. They also had a substantial union presence.
This is less true today as wages and conditions in these industries have worsened considerably, as they became almost entirely non-union. At this point, more immigrants are likely to primarily depress the wages of other immigrants working in these sectors, although if there had not been a sharp uptick in immigration over the last three decades it is reasonable to assume that these industries would still employ native born workers at a better wage than they would have been able to receive in other industries.