(Note: As I keep reiterating, Democrats, "progressives," and leftists may well be decent people in their private lives, but then become something much different in politics.)
I googled different variations of the question: one, two, three. The results weren't illuminating. But I had hoped that I might find some defender of Democrats who took this question on in order to refute it. Had this happened, wouldn't we have heard about it really loudly from Democrats by now? Wouldn't their social-media network have done their usual linking-on-the-very-day activity so that we'd all be hearing about it? Because it's something Democrats should do, for sure, in order to allay the suspicions that they're fighting Trump on this for the political advantage they might be, appear to be, getting from the presence of millions of illegal immigrants in the country.
One reason this is a perfectly legitimate question to raise in this context is a table-turning one: Democrats impugn the motives of Trump and his base on this issue all the time. It's about xenophobia and fear-mongering and racism and, well, Republican hopes that stemming the tide of illegal immigration would benefit them politically, in the longer-term, as "future Democrat voters and/or Democrat voters who sympathize with illegals" are stymied by "better border security." "Better border security" is the basic rationale that Trump offers, but Democrats don't believe him; they keep falling back on "Trump is fear-mongering" (Schumer in his response to Trump's oval-office appeal yesterday) and "this isn't in accord with our values/morality." (Would Democrats really benefit politically from a debate on values/morality? Do they really want to go there?) One clue to the way Democrats poison the dialogue on this is to muddy the distinction between illegal and legal immigration. Trump keeps saying over and over that he welcomes and invites people to come into the country legally - with a very pointed intonation in his voice on that word - but this hasn't stopped Democrats from painting him as being anti-immigrant, xenophobic, etc. (That itself should make one question their sincerity.)
Republicans keep pointing out that Democrats were in favor of beefed-up border security before Trump came around and now they oppose it (a) in order to deny Trump a political win, and/or (b) a "yes" answer to the topic question this post is addressing, and/or (c) the Democrats have become more and more radicalized politically in just a few years (for which claim there are data).
Are Democrats behaving in the way they would if they saw a long-term political advantage in illegal immigration? In addition, are they behaving the way they would if they had values and ideology that are out of step with much of the rest of the country? The questions are not unrelated to one another, either, even though one points to political advantage and the other to values/ideology. Conceivably, the Democrats could knowingly and willingly do one of these two things at the expense of the other. But I rather doubt that it's working out that way; there seems to be a "happy" convergence between these two things and they don't seem to face a set of incentives that would break these two things apart in their MO. Either option is pretty troubling even if the motives are less clearly corrupt in one case than the other.
One piece of evidence that illegal immigration isn't good politically for Democrats, short term: the election of Donald Trump. The Republicans and especially Trump are behaving in the way they would if they saw long-term political disadvantage in illegal immigration, as well as a converge between that and values/ideology they have which may be out of step with CA and NY but perhaps not those of swing voters in PA, MI, and WI. It could be that if Democrats do seek long-term political advantage in illegal immigration, that Trump serves as a roadblock to that but they hope for a long-term victory.
One reason to bring these kinds of questions up, is the amount of money that separates Democrats and Trump and keeps them at an impasse while the federal government remains partly shut down. We are talking something on the order of $3 billion. The annual federal budget is something on the order of $4 trillion. We're talking a one-time appropriation that is one tenth of one percent of the annual federal budget. It doesn't seem to make much sense that the two opposing parties would make that big a deal over this amount of money unless something considerably more than $3 billion worth were at stake. They each appeal to values and ideals but if they're transparent they should also address the issue of political advantage.
There is the further question: let's say that there is motivation by political advantage going on with both sides. But which party's motivations aligns better with the interests and values of the American people? One of those values concerns the importance of the rule of law, of having people in the country who don't break the law to come and to work here. Democrats in hardcore Blue States, meanwhile, have set up sanctuary cities which have the effect of shielding what appear to be important Democrat constituencies from the legal accountability that Republicans want to apply to them. Upon Googling 'sanctuary cities' the first link I clicked on was an MSNBC link that claims to debunk Trump and the GOP's depiction of the sanctuary-cities situation. But as if to make Trump's very point for him, here's what a picture caption in the article states: "Agung, an Indonesian man who lives in south Philadelphia, is a rising leader in the city’s new sanctuary movement. He is helping with a campaign to grant driver’s licenses to undocumented immigrants." And now just yesterday we get this headline: New York City mayor vows health care for all — including undocumented immigrants. (Isn't this evidence that NYC's mayor benefits politically from illegal immigration?)
Now, Democrats speak of the need to solve practical problems that arise when undocumented (illegal) immigrants try to access healthcare systems, roadways, and other public services. We can't turn away sick people from hospitals, practically or morally, can we?
It sure sounds like typical Democrat values-mongering that so much of the rest of the country looks upon with suspicion and revulsion. Whatever their motives, these sorts of measures implemented or proposed by Democrats make it easier for people to be in the country illegally. (They seem to be similarly tone-deaf when it comes to their "anti-poverty" programs generally: their programs do make it easier to be and stay poor, with the incentives that go along with this and the very disappointing results that have come from more than half a century of their Great Society "war on poverty" programs. Similarly, they make it easier to be a government employee, through things like pension promises that aren't necessary to clear the public-employment market. In Democrat-think, the relative job security of a government job should come with a premium rather than a discount. Etc.)
All in all, it would seem that Democrats would prefer to drag their feet, one way or another, in addressing the country's illegal-immigration problem. Their values-rationales aren't accepted by much of the country. Politically they don't seem to face much in the way of disincentives, certainly not within their own states, to keep illegals out; if anything, their incentive structure tells them to basically invite illegals on in with the promise of sanctuary and/or benefits. Their flipping out over $3B aimed at stemming the flow of illegals and/or drugs into the country looks suspicious. Trump claimed in his Oval Office address yesterday that the increased border security would pay for itself many times over just in terms of the flow of narcotics that would reach fewer American streets/hands. Is that untrue? (Well, it is Trump, so there's not exactly a presumption of truth or accuracy when he says a lot of things. However did he manage to get elected, if not for his opposition?)
In any case, I don't think we can have a transparent discussion of the subject of illegal immigration without bringing well out into the open the topic of who benefits politically from what - in addition to the values-questions that do motivate much of the debate. As to those values-questions, there's nothing I've seen that would demonstrate Democrats' moral superiority on them, their well-known pretensions to intellectual and moral superiority notwithstanding. If anything, just the reverse. As to their political motivations, they pretty much blew whatever credibility they had (politically as well as intellectually) with their obviously politically-motivated smears of now-Justice Kavanaugh, and their ridiculous attempts to normalize those smears epistemically. There's good reason not to trust them, their ideas/values, or their motivations at this point. (As I keep reiterating, they may well be decent people in their private lives, but then become something much different in politics.)