I think your understanding of the University of Michigan’s finances is flawed. Michigan has the 9th largest endowment of any school, public or private, at just over $10 billion. It was weaned away from substantial legislative appropriations a generation or more ago, beginning in the 1970s when the U.S. auto industry was in a deep crisis, leaving a huge adverse impact on the State of Michigan’s tax revenues. State appropriations to the university never really recovered–they now stand at less than 5% of the university’s total operating budget-- so the university had to find other ways to fund itself. Together with the University of Virginia, Michigan has over the last 30-40 years pioneered a public/private hybrid model, building up a huge endowment, building its research capacity to the point that it now has total research expenditures of $1.3 billion annually, most of it externally funded (second only to Johns Hopkins, a special case because JHU gets to count the Applied Physics Laboratory, a very large research lab generously funded by DOD and NASA but administered by JHU), and increasing the percentage of OOS and international students in its student body, most of them full-pays at tuition rates similar to those charged by elite private colleges and universities. Recent entering classes at Michigan have been a shade over 40% OOS and international. As a consequence, notwithstanding relatively paltry contributions from the state, the University of Michigan’s finances have never been in better shape. It is one of a handful of public universities that meets 100% of need for 100% of state residents with demonstrated need, and it is now committed to a goal of meeting 100% of need for OOS students as well, something it will be able to accomplish once it completes its current $4 billion capital campaign—the largest in the history of public higher education—which will further swell the size of its endowment. As of November, 2014, one year into the capital campaign, the university had raised $2.5 billion in new gifts and pledges, well on its way to meeting or exceeding its ambitious goal.
Not to pick on Illinois, but the contrast is striking. At $2.3 billion, the University of Illinois’ system-wide endowment is less than 1/4 the size of Michigan’s, for a 3-campus system with 60% more students than the University of Michigan. UIUC meets full need for only 10.8% of its students with demonstrated need, according to its latest Common Data Set. and on average only 64% of need is met. These are markers of a much more resource-constrained environment.
There are many reasons public universities don’t do as well as privates in the US News rankings, not least because those rankings reward a high cost-per-student educational model which punishes publics for the economies of scale they can achieve. Note also that the metrics US News uses have been revised repeatedly since the 1980s. But the suggestion that the University of Michigan has fallen in the US News rankings because of state budget cuts and faltering finances is just wildly off-base; nothing could be further from the truth.