It's not necessarily pubic programs that are the problem. Unemployment among low-skill workers is still high[1]. I don't see how increasing competition for unskilled jobs is good for those already struggling workers suffering from a low-skill labor glut. And intuitively I'd expect high-skilled workers to generate more complementary jobs than low-skilled ones.

Today's economy and the economy in 1920 or even 1960 don't much resemble each other. For starters, the costs of labor regulation and employer mandates sets a pretty high price floor on labor. That creates a much more difficult market for workers with relatively low marginal productivity to find work.

Also, the population has a far more top-heavy age distribution than it used to have. This country is going to need a very productive labor force to maintain the welfare state at anything close to the current tax levels.

[1] http://c4.nrostatic.com/sites/default/files/YL%20chart.jpg

They are a net positive not least because they are willing to work for less thereby depressing average wages. Great for the economy, even better for employers. Not quite as great for employees.

I won't bother to call "[citation needed]" on this since I'm sure there are biased analyses out there on both sides, but consider lifetime cost vs. working years remaining. Maybe we're economy-positive on an 18 year old unskilled laborer, even. But most pro-immigration policy changes involve a lot of older folk coming along with in the long run, and not everyone who comes and stays makes enough to be a net positive from a tax POV (not even considering the retirement/medicare time bomb).