What they'd said (in the recent PBS piece) about the 'trends' of support rising and falling has some evidence behind it. It's based on a recent 'Gallup' opinion poll that puts support of increasing "immigration" at 28%, and "LEGAL immigration" at 34%. The questions were phrased differently for about half of the sample each. But it is what it is - an opinion poll of about 1,500 persons. They appeared to also do some basic weighting of demographics. What I found interesting about the poll as well was that the percentage of respondents who said immigration should "stay the same" has stayed fairly level over time. Looking at the graphic as well, there are "peaks and valleys" throughout; so even though "increase" is on an upward trend, it has been before, has leveled off, and has fallen.
I think, too, the current "climate" should be considered in interpreting numbers such as this. So this "record high" as Gallup calls it, shouldn't really be so surprising
Record-High 75% of Americans Say Immigration Is Good Thing