I just made up the scale, but that seems to be the jist of the argument, and if that's what you're saying, then I think you're wrong. I think we can help those people more than we'd hurt anyone at home.
In fact, most studies point to the positive economic impacts of immigration over time (though there are a number of studies that also point to the short term costs).
I think that the united states could absorb the entire population of Haiti without much impact (ie., from 81 to 80), and eventually we'd probably benefit. But how about all the desperately poor people everywhere else in the world? At some point, I think we're going a lot further down than just one point on the scale.
Right now, this reality is reflected in our (remarkably badly run) immigration system, where the United States takes about 1.2 million immigrants legally into the country every year, by far the most in absolutes and high up there in percentage of population, but still faces a surprising amount of criticism for being anti-immigrant because we don't take in even more. Much of this criticism comes from people who live in countries that are remarkably stingy with their immigration systems.
I doubt that statement, too.
That said, do you really think that "unrestricted" immigration (excluding border cases of known criminals, etc...) in the US (or Canada, Australia, etc) would not have a substantial negative impact on quality of life? It seems obvious to me that it would, but if you have any good arguments, studies, links to the contrary, feel free to post - I will read them.
Yes, I do believe that unrestricted immigration would not have a substantial negative impact on quality of life for the resident population. And would have an enormous positive impact on the migrant population.
People from the poorer parts of the US are already allowed to migrate to the richer parts. Why stop there? Also as poorer nations joined the Schengen-Area (related to the EU) there have not been qualitify-of-life-decreasing mass-migrations.
You may argue that there can be quality-of-life degradations when the immigrants are not properly integrated. But the US seems to do a pretty good job in this respect. (My home country, Germany, much less so.)
Sorry, I do not have enough time to write down a real argument, but if you are really interested, I can perhaps prepare a blog post or so.