I've written about public opinion on several aspects of immigration, but there is one that I haven't considered: whether decisions about who to admit should give more weight to "merit." This issue also hasn't received much attention in surveys, but in 2007, 2013, and 2017, there was a relevant question: "When the US government is deciding which immigrants to admit to this country, should priority be given to people who have family members already living in the US, or should priority be given to people based on education, job skills and work experience?" The overall distribution of opinions:
2007 34% 51%
2013 28% 59%
2017 44% 46%
The difference between times is statistically significant. There also are shifts in the relation with partisanship--I show the percent saying family minus the percent saying education, skills, and experience:
R D I
2007 -29 0 -22
2013 -30 -25 -38
2017 -29 +20 -3
Republicans were almost exactly the same at all three times, but Democrats and Independents moved towards education and skills between 2007 and 2013 and then towards family between 2013 and 2017. Another way to put it is that there were moderate differences by party in 2007, small differences in 2013, and large differences in 2017.
I don't remember if immigration policy was particularly in the news in May 2007 or April 2013, but in August 2017 the Cotton-Perdue bill, which would shift the priority away from family ties and towards skills, had just been introduced. My guess is that Democrats and independents were reacting against the proposal, but that raises the question of why Republicans didn't move in favor of education and skills. It may be because Donald Trump hadn't emphasized the issue in his campaign or his presidency up to that point--he'd focused on illegal immigration and vetting for terrorist sympathies. So Democrats may have been more sensitive to proposed changes.
In the last few months, Trump has started pushing for changes in immigration law; ending "chain migration" and the "lottery system" have become two of his favorite twitter themes. So if this question is asked in the near future, I think Republicans will shift in favor of skills, and Democrats and Independents will shift further against it. I also think that overall support for skills will decline, because Trump's remarks last week linked the issue to race in the public mind. A shift to skills would almost certainly shift the composition of immigrants towards whites. However, although the idea of a skill-based system had been discussed by people who were interested in public policy, it hadn't received a lot of news coverage, so the average person answering the question probably didn't think about this implication. Blacks were more likely than whites to favor family ties, but the difference was small (43.5% vs. 36%). But after last week, race will be the first thing that many people think about; maybe his base will move towards favoring skills, but blacks, Hispanics, and many whites will move in the other direction.
[Data from the Roper Center for Public Opinion Research]