A few comments on the NY Times article on the subject.  I preface this by saying that I’ve never met Obama, he was not teaching when I visited there, and I’ve not discussed the article, or their experience with Senator Obama, with any of my new colleagues.

From the Times:

At a school where economic analysis was all the rage, he taught
rights, race and gender. Other junior faculty dreamed of tenured
positions; he turned them down. While most colleagues published by the
pound, he never completed a single work of legal scholarship.

Economics is still a powerful analytical tool and influence for many faculty at Chicago, but during the time Obama taught "rights, race and gender" at Chicago, various tenured members of the faculty (Mary Anne Case and Martha Nussbaum, among others) were doing so too. 

At a formal institution, Barack Obama
was a loose presence, joking with students about their romantic
prospects, using first names, referring to case law one moment and “The
Godfather” the next.

Chicago just ain’t that formal!  Or maybe everyone was playing "laid back" when I visited!

Mr. Obama, now the junior senator from Illinois and the presumptive Democratic presidential nominee, spent 12 years at the University of Chicago
Law School. Most aspiring politicians do not dwell in the halls of
academia, and few promising young legal thinkers toil in state
legislatures. Mr. Obama planted a foot in each, splitting his weeks
between one of the country’s most elite law schools and the far less
rarefied atmosphere of the Illinois State Senate.

We shall hopefully find out if these experiences enhance Presidential performance.

The Chicago faculty is
more rightward-leaning than that of other top law schools, but if
teaching alongside some of the most formidable conservative minds in
the country had any impact on Mr. Obama, no one can quite point to it.

“I don’t think anything that went on in these chambers affected
him,” said Richard Epstein, a libertarian colleague who says he longed
for Mr. Obama to venture beyond his ideological and topical comfort
zones. “His entire life, as best I can tell, is one in which he’s
always been a thoughtful listener and questioner, but he’s never
stepped up to the plate and taken full swings.”

Chicago certainly has been more libertarian/free-market-utopian leaning than Yale, Harvard, or Stanford, but whether that is true today and will be true tomorrow is a different matter.  If one is looking for an unusually large number of "conservative" law professors–not libertarians like Epstein–Northwestern, among the top 15 law schools, really stands out more than Chicago these days.  Economics remain an important influence in much faculty scholarship, but that isn’t the same thing as "rightward-leaning" anymore.  And it does puzzle me a bit how a school with very high-profile liberals like Martha Nussbaum and Geoffrey Stone–as high-profile as any in the legal academy–still gets pegged as "rightward-leaning."  (The school has even been known to appoint faculty with a sympathetic interest in Karl Marx, for God’s sake!)  Of course, as I noted on an earlier occasion, "Willingness (and ability!) to mix it up in vigorous intellectual combat
is the hallmark of the school, not political ideology. This is as true
for the faculty as the student body."   

The Chicago law faculty is full of intellectually fiery friendships
that burn across ideological lines. Three times a week, professors do
combat over lunch at a special round table in the university’s
wood-paneled faculty club, and they share and defend their research in
workshop discussions. Mr. Obama rarely attended, even when he was in
town….

Several colleagues say that Mr. Obama was surely influenced by the
ideas swirling around the law school campus: the prevailing
market-friendliness, or the use of economic tools to analyze the impact
of laws, for example. But none could say how. “I’m not sure we changed
him,” Mr. Baird said.

Because he never fully engaged, Mr. Obama “doesn’t have the
slightest sense of where folks like me are coming from,” Mr. Epstein
said. “He was a successful teacher and an absentee tenant on the other
issues.”

No coment, just noted.  I guess time will tell on this one.