I've done my own research. And I haven't been able to find prominent Democrats suggesting any kind of restriction on legal immigration.
Thanks for the Sanders example. I missed it the first time, since it looked separate from the rest of your post. It is worth noting that his comments are mentioned as controversial within the Democratic party, and that he isn't officially a Democrat. He also remains vague on how many people he wants in the country legally each year.
Immigration (the umbrella term for border enforcement, legal immigration policies, and how we handle people here illegally) is definitely a major issue. We are dealing with 11,000,000 people who are here illegally, who would stand to benefit from some kind of amnesty. They have family.
There are also the people who want to come into the country. There are about 1,000,000 legal immigrants an year, with a total of 37,000,000. There are millions on various waiting lists. With a generous enough admissions policy, you could conservatively estimate that tens of millions of people in the world would like to be Americans if the barriers to entry were removed.
Some places are going to be more affected than others by the new additions. They're going to need all kinds of support (IE- language services for children in school) and handling the situation right will determine whether millions assimilate into the upward class or marginalized lower class groups.
It's also untrue that this is an issue that started with Trump. It's been an issue before that. Pew has polled Americans on the topic since 2001, and the number of people who want immigration decreased has gone from 53% to 24%, while the number of people who want immigration increased has gone from 10% to 32%. Meanwhile, the amount of people who want the number of legal immigrants to be the same has been consistent.
http://www.people-press.org/2018/06/...-into-the-u-s/
It's worth noting that only 40 percent of Democrats want immigration to increase. So this isn't even a majority position for the Democratic party.
https://www.usnews.com/news/politics...g-both-parties
If immigration hadn't been a controversial issue, there would have been more significant revisions to immigration policy under Bush or Obama.
It can be argued that this is an issue that most establishment politicians weren't willing to touch, although it becomes a problem when there isn't anyone running who matches the policy goals of a significant percentage of the voters.
I don't really follow conservative pundits. The idea that Democrats are essentially advocating for open borders has been coming from analysis from left-wing writers.
https://www.theatlantic.com/magazine...istake/528678/
https://www.vox.com/2014/9/13/613590...iew-gdp-double
Disproving the idea that Democrats are pushing for open borders should be pretty easy: they should be open about the upper limit for admitted immigrants. But if they're vague about the existence of an upper limit, they're basically advocating for open borders. It does seem members of the Democratic party have decided to be vague on their actual views on legal immigration. I'm drawing the strongest negative inference from that.