That's unfortunate news.

There's no recourse I can think of these days.

"As January 8th 2007 all US and Canadian citizens will need a passport for their Mexico visit; if a USA resident, your resident (so-called "Green Card" in US) card and passport will be required. (A drivers license and birth certificate are no longer valid forms of identification for a visit to Mexico when travelling by air.) If you arrive at your departure airport without a current valid passport with at least 6 months remaining from your date of entry, to match the 180 day maximum period your FMM is normally valid for, your airline may deny boarding. (Those arriving by ground may use a birth certificate with raised seal of authentication AND photo identification), but if by air passport only.)"

The sticky thread "Requirements for visiting Mexico as a tourist (FMM, "tourist card", visa, etc.)" has links to TIMATIC, etc. that reinforce the above.

The onjy option I can think of is to fly to San Diego, cross the border by land using the normal San Ysidro or Otay Mesa crossing (better: taxi or transport to the CBX bridge at Otay Mesa (link), where crossing by land she'd be allowed if she has her ODL and a raised seal / embossed birth certificate. She could then fly to her original destination in Mexico domestically via Aeroméxico, Interjet, etc.

A bit elaborate and still slightly risky, so it might be more practical to postpone her departure flight until the new passport is in her hands. (There'd likely be a change fee, but this might be best - though it's harder to do without knowing when USDOS will release her passport).