All this talk of "Offer her the VP position" (I would bet money against this happening) or "Offer her SCOTUS" (seems better odds) or "Offer her Senate Majority leader" (not Obama's to offer, and probably within reach for Clinton anyway) misses the point to me.
First of all, Clinton and her advisors know full well that her odds of securing the nomination are minuscule at best. They're soldiering bravely onward not to gain the shot at POTUS, but to gain political leverage. Nothing wrong with that; anyone would do the same.
So what is it they want?
I don't think she wants VP, nor do I blame her; SCOTUS seems long odds and doesn't fit with her style of public service (Not to mention that she, and Bill, love campaigning and the whole political business that the judiciary lacks. And majority leader only matters if you have something to do.
She is, however, a policy wonk, and she has had one primary issue for decades: health care.
Most Obama supporters I know will agree this is where she takes him, hands down - her plan is simply better. And she cares about it deeply, she knows the politics of it, she's had a run at it before. Let her take it on again.
Obama should offer to back Clinton's health care plan, giving her full credit and letting her run the legislative campaign. It would strengthen his support with his own supporters, help reach out to hers, and shore up a weak spot in his platform.