Cato did a study in 2017 that asked people if they supported immigration. Most people did. Then they asked people what they thought the level of immigration should be. The median answer was around 500,000 a year. The real level is 2-5 times higher than that. That’s why nobody will push for a real skilled immigration system. Once you open up the issue to public debate, a likely outcome will be a demand to drastically cut the level of legal immigration.
For example, right now, nobody is thinking of how many immigrants come to the U.S. through family unification for each H1B worker that eventually gets permanent residency. If you open up the issue now it’s going to become a firestorm when people realize that “65,000 skilled workers a year” actually results in millions of people every year, most of whom aren’t skilled workers.
How does 65000 workers translate to millions of unskilled relatives? Even green cards for relatives are a nontrivial process.
I can't find the study in question, but I'd be interested in the polling process. The average person has zero understanding of what 500,000 immigrants per year means. For context, the average American is off by at least a factor of 2 about the population of the United States. If the questioning wasn't something along the lines of "of the people you personally know, what fraction should be immigrants" or something, I have no idea how you'd get anything resembling useful responses.