It's likely that the next president will face at least one Supreme Court vacancy. Obama should promise Hillary Clinton, now, that if he wins in November, the vacancy will be hers, making her first on a list of one.
Obama and Clinton have wound up agreeing on nearly every major issue during the campaign; at the end of the day, they share many orthodoxies. Unless the Supreme Court were to get mired in minuscule details of what constitutes universal health care, Obama could assume that he'd be pleased with most Clinton votes, certainly on major issues such as abortion.
Obama could also appreciate Clinton's undeniably keen mind. Even Clinton detractors have noted her remarkable mental skills; she would be equal to any legal or intellectual challenge she would face as a justice. The fact that she hasn't served on a bench before would be inconsequential, considering her experience in law and in government.
If Obama were to promise Clinton the first court vacancy, her supporters would actually have a stronger incentive to support him for president than they would if she were going to be vice president. Given the Supreme Court's delicate liberal-conservative balance, she would play a major role in charting the country's future; there is no guarantee that a Clinton vice presidency would achieve such importance.
Despite its infatuation with "activist" judges, the right's response to the Clinton years was Scalia throwing the 2000 election, followed by Roberts and Alito.
This inspired idea has the delicious aroma of karma about it. Much better than VP — Justice Hillary Clinton!