In 1997 a Pew survey asked "if you were making up the federal budget this year, would you increase spending, decrease spending, or keep spending the same for...." In 2011 it asked almost the same question, just substituting "budget for the federal government" for "federal budget." Ten items were asked in both years, including "financial aid for college students." I summarize the results by giving percent who said increase minus percent who said decrease:
1997 2011 change
The public school system 60 43 -17
Combating crime 55 21 -34
Health care 50 17 -33
Financial aid for college students 43 28 -15
Social Security 37 29 -8
Medicare 36 28 -8
Environmental protection 32 10 -22
Scientific research 31 13 -18
Military defense -9 1 +10
Government assistance for the unemployed -13 -1 +14
Support for spending on most programs was lower in 2011 than 1997, which I think was because there was more concern about the budget deficit. But the drop for financial aid was not especially large. It was the fourth most popular program in 1997 and tied for third in 2011.
So there's no evidence that the declining value of Pell grants reflects lack of popular support--I would guess that it's a consequence of the general squeeze on discretionary spending. As far as the popularity of different spending programs, my hypothesis is that it's about whether the recipients are regarded as "worthy" rather than whether they are means tested. Old people and students are regarded as worthy. So are the working poor, which explains why programs like the Earned Income Tax Credit don't encounter much opposition. Programs that help working-age people who don't have jobs are a different story.
*There were no links to sources, so I don't know who compared recipients of financial aid to welfare recipients. I haven't read "Academically Adrift" but from the reviews it sounded like its criticism was directed more at colleges and universities than at students who received financial aid.