Ukrainian-American comedian Yakoff Smirnoff once said that when he became a naturalized American citizen the first thought that entered his mind as an American was "I hate these foreigners. They come here and take our jobs!"
And of course that's a concern a lot of people have, and not just on the low end of the income scale. Software developers and engineers have complained for some time that they used to make more they had to compete with an influx of foreign workers admitted under the H1-B visa program for highly skilled guest workers. (The H1-B program has been criticized as being unfair to foreign workers as well, since the visa basically ties them to a single employer who can threaten them with deportation.)
But economists across a broad political spectrum tend to agree that immigrants are a net economic benefit to the country. Yes, they compete for jobs, but they also spend money, which creates more demand and results in economic growth. Here's a segment on that from the Crash Course Economics web series: