One very common (and bi-partisan!) argument I see against immigration is that it will lower wages of American workers. This meme is, fortunately, nonsense, as confirmed by numerous actual studies of real-world data. It is a classic example of what economists call the "Lump of Labor Fallacy" - the idea that there is a fixed pool of jobs, and if someone gets one, someone else does not. While this might be a sensible notion in one's very narrow experience, it is not true in the broader economy. If someone beats you out during the final interview round for a job, it is true that in the very short term, you are still out of work. However, the number of jobs in the economy does not decrease by one. Why? Because that someone will presumably spend their money from their new job, which will in turn create approximately one new job. If there were a million open positions across the US before the final interview round, there will still be a million the next day.
Immigration works the same way. Assuming for a moment that immigrants are more or less demographically matched to the native population in terms of education, age, etc, then any jobs they "take" will be made up for by the jobs they create when they spend their earnings. At first principle, this is a wash. In reality, immigrants are not demographically matched, so they can have impacts in specific labor markets where they are concentrated. If, for example, we were to allow a million dock workers to immigrate to the US, it is obvious that the wages of dock workers would fall. However, this would mean prices for goods passing through the docks would fall, which would in turn mean we'd all have a few more dollars in our pockets each month. When we spend this money, we'd create jobs all throughout the economy. How many? About as many as were lost by native dock workers! Likewise, the push to import a bunch of STEM workers will almost certainly depress wages for native STEM workers, but it means everyone else will be getting STEM products for cheap, saving us cash that we can then spend on other things. So while STEM workers have a right to complain, and may even deserve some sort of compensation or protection, overall, society wins.
If you can't see my point, let's try it another way. It should be obvious that population size of a country has essentially no impact on wages - there are plenty of counties of all sizes which are rich, and plenty which are poor. Therefore, to claim that immigration can lower wages is to claim that the economy somehow differentiates between population growth via border crossings and population growth via vagina crossings. That, of course, is absurd.