Facebook's COO is mounting yet another PR offensive. But not on behalf of her current employer, though it could use some good press. No, Sheryl Sandberg is defending former boss Larry Summers against charges of sexism . Summers, who was Treasury Secretary under Clinton, is being talked up for the same role in Barack Obama's Cabinet . A controversial speech Summers gave as president of Harvard University — speculating that innate differences might have to do with women's lack of progress in math and science — could ruin his chances. Hence Sandberg's timely defense.But the defense is timely for Sandberg as well. Sandberg served as Summers's chief of staff before she moved to Silicon Valley and joined Google, setting her up for her current job at Facebook. Summers and Sandberg had a close professional relationship; he even escorted her as his guest to a White House dinner in 2000. At Google and Facebook both, colleagues roll their eyes as they recount how often she brings up her Washington experience and brags about how working in tech is a cakewalk compared to D.C. But Sandberg's tenure at Facebook has been controversial. She's been acting as if she's the company's No. 2 executive, despite CEO Mark Zuckerberg's reassurances that her role is limited and she's not a CEO-in-waiting. Several key tech and product executives have left since she's arrived — and, crucially, she has not made visible progress in improving the company's ad-sales operations. At least one prominent investor has been talking about "reining her in." So why not head back to D.C.? If Summers gets the Treasury job, he'll surely call on Sandberg for advice, and perhaps more. Will she be able to resist the call to public service? Her husband, Dave Goldberg, is an entrepreneur-in-residence at Benchmark Capital — a placeholder job he could easily leave. Her children are young enough that she could move back east without disrupting their schooling. It might be a now-or-never opportunity. It must be on her mind — and on the agenda at Facebook's next board meeting. Sandberg leaving Facebook for the government gives everyone a graceful out from a bad situation. Zuckerberg could help give her a nudge; his cofounder, Chris Hughes, was the director of Obama's Web campaign. Perhaps he could put in a good word for Sandberg? If Summers gets the Treasury job, the only question is whether, having made millions at Google, she really wants to work as hard as she tells everyone she used to.