In the same way that saying “they are eating the cats” is a bullshit that wants to demonize all immigrants, thinking that if you put in millions of immigrants in a short period of time without background checks they will all be wonderful people who will not cause any problems is another bullshit. And I believe that in the case of the Democrats they do it from a business perspective as I explained above, it is a way to buy voters.
Immigrants can't vote until they're citizens. Contrary to popular belief in some qanon circles, there is no fast-track citizenship for asylum seekers (which is I think what most anti-immigration rhetoric is focused against). They have to apply for permanent resident status, which comes with all background checks and everything else that any permanent resident has to go through. There is even a medical exam involved for some reason. After that, getting a criminal conviction can result in deportation. Even something as benign (for a citizen) as DUI or being homeless can mean deportation (for a permanent resident). At the end of all this, after 5 years, one can apply for citizenship. Once they have it, I don't know why they would need to vote for one party or the other. But if one party claims they're eating dogs and cats, I can see how they might be reluctant to vote for it.
The US needs ~1 million immigrants every year just to sustain population size and economic growth. Trump killed immigration reform bill so that he could continue to use this issue as a campaign slogan. That's pretty much all there is to know about his immigration policies.
If the goal was to somehow increase the "quality" of immigrants so that that don't cause "problems", Trump and his party are really terrible at expressing those ideas because I haven't heard anything of the sort. The reality is that they just want to rile up the base against brown people without explicitly saying so.
If the goal is stop immigration or slow it down that only certain demographics can come in, then they will kill the economy but that's again just another can down the road.
IIRC ~100 million Americans are first or second generation immigrants, and they tend to be (particularly 2nd gen) around average or better than average on metrics like income, education, crime, etc and tend to vote similar to other people in their age range, so it seems that the evil Democrat plan to buy votes is a big failure.
This country was built on immigration and hopefully with continue to be, otherwise we're all fucked and not in a pleasant consensual way.