So was Obama ever offered a tenured position at the University of Chicago Law School

This is a pretty incredible claim.  Clearly the New York Times reporter ignored what she was told by Richard Epstein on this score.  Nor was it the only thing that she did report in her generally glowing article on Obama.  I was also interviewed by Kantor in 2008 about my experiences with Obama and she didn't use any of the material that I gave her because Obama's campaign simply asserted that the conversation didn't happen.  From the Daily Caller:

“Other faculty members dreamed of tenured positions; [Obama] turned them down,” wrote Times White House Correspondent Jodi Kantor, author of “The Obamas,” in a July 30, 2008 profile of the president’s twelve years as a lecturer at the University of Chicago Law School.

And yet, according to longtime University of Chicago law professor Richard Epstein, Obama was never actually offered a tenured faculty position.

“I have no idea where Jodi got her story” about the tenure offer, said Epstein, adding that he immediately wrote Kantor to tell her she was wrong. Epstein was, then, a member of the faculty, not the school’s dean. . . .

Kantor softened her position when asked via Twitter about Obama’s alleged tenure offer.

“[T]he general idea was that tenure would go through,” Kantor replied. “That said, I don’t know the fine print on the offer.” . . .

“I wish I still had my email to Jodi,” he lamented, “because I wrote Jodi Kantor in no uncertain terms that the matter had never come to the faculty, and that under no circumstances would an offer to Obama be tenured. Indeed I was completely taken aback by the story.” . . .

It is hard to see that Obama could get a tenure track position, let alone a tenured position, from the University of Chicago.

Of his 12 years as a lecturer at the University of Chicago Law School, Time Magazine said in 2008: "Within a few years he had become a rock star professor with hordes of devoted students."  But student evaluations obtained by the Examiner tell a different story. In 2003, only a third of students recommended his courses.
"It went steadily down in the last five or six years that he was there. He was among the lowest-ranked professors," Tapscott said.
Nor did the future president leave any record of scholarly writings, while similarly credentialed colleagues had a prolific presence in law journals.
"He showed up to class, he gave his lectures and he was gone," Tapscott said.  . . .