Increase supply of labor, decrease wages. Econ 101, folks. The Wall Street types benefit from immigration. There might be "more jobs" but there will be lower pay checks. Working Americans are the targets in this upper class scam. Polls show that most Americans are for moderating immigration. Strangely, rich Democrats are the ones most for open borders and "free" trade. The party of labor? No way.
Decreased wages for those who have jobs, plus more people having jobs, might be an excellent tradeoff even if it wouldn't appeal to a 100% selfish person who has a job and doesn't fear losing it.
And you need to be awfully careful about what "polls show that most Americans are for". For example, polls show that most Americans would like to see US foreign aid reduced from about 25% of GDP to about 10% of the federal budget. The trouble is that the actual level of US foreign aid is about 1% of the federal budget. So, do "polls show" that most Americans would like foreign aid cut by 2.5x, or that most Americans would like foreign aid increased by 10x? -- In the absence of more information about what "most Americans" actually think the level of immigration is, and what they think its impact is, polls purporting to show that most Americans would like more or less immigration are pretty uninformative about what would actually benefit most Americans, or what they would choose if they had better information.
It would be better to keep party politics out of this. (Though from what you've written I wonder whether party politics are your only reason for being interested in the matter at all.)
