To be clear, though I support immigration in a controlled manner, I do not believe in any loony leftist variant of open borders, and believe a nation is defined (at least in part) by its borders, and should be. Therefore, I strongly support:

1) Border controls

2) Turning people back at the border

3) Rounding up and deporting those in the country illegally

4) Mostly allowing desirable immigrants in (those with special skills, etc.)

5) Pretty much denying entry to all economic migrants (more than 80% of immigrants)

6) Very importantly, strongly prosecuting the CEOs and other C-level execs of companies that hire illegal immigrants to do jobs that American citizens and green card holders should be doing

Open borders and even accepting everyone who wants to show up can only work if the in-flows and out-flows are roughly equal. Furthermore, a generous welfare state can probably only work if there is not huge amounts of immigration (politically). For this reason, I do not buy 90% of the leftist immigration talking points, and believe that it is mostly just poorly-repackaged corporate propaganda masquerading as liberalism.

(Observe how most of them spend so much time prattling on about immigration, but very little time protesting military entanglements overseas, or our policies and actions in Central America which cause a lot of immigration, etc.)