Hanging over her head, as well as the heads of other GM executives, could be a criminal prosecution, just like the one that pressured Toyota last week to agree to a $1.2 billion fine and three years probation. Not that the government definitely intends or is likely to charge her — but, hey, who could take such a chance by showing anything but remorse?

Once the klieg lights and TV cameras are switched on, anything might happen. More than a few members of Congress bear a grudge over facets of the 2009 GM bankruptcy, including the way it was used as an instrument — remember “Let Detroit Go Bankrupt”? — to undermine Mitt Romney’s presidential bid.

MORE: GM’s recall scandal: A scorecard on Mary Barra

GM has more or less already pleaded guilty to the charge that it was too slow to fix an ignition problem it first learned about in 2004 — and perhaps as early as 2001. The affected Saturn Ions and Chevrolet Cobalts numbered about 1.6 million. In the meantime, 12 deaths and 31 accidents have been attributed to the faulty ignition. The problem evidently could be triggered when a heavy keychain inadvertently jarred the key from the “run” position to “accessory,” disabling airbags and other safety equipment.

Remorse didn’t work so well for Toyota (TM). The company’s president Akio Toyoda in early 2010 apologized profusely before Congress for a series of accidents involving the automaker’s vehicles. The affected cars were alleged to accelerate without pressing on the gas pedal, rendering automobiles uncontrollable. Four years later there’s little evidence that an obvious defect was responsible apart from some customers placing multiple floor mats in front of the driver, which in some instances entrapped the gas pedal.

Toyoda expressed sorrow for accidents and condolences for the victims — the company did not concede that negligence or deliberate acts of malfeasance caused the accidents or that it intended to hide evidence.

Toyota had learned from customers in Europe and the U.S. that some of their accelerators were “sticky.” It corrected the potentially dangerous problem with a recall, though no accidents or injuries were attributed to it. A third allegation, that electronic “gremlins” were the blame for wild acceleration, baffled researchers and finally was deemed to be spurious. What’s more likely is that some older drivers, as in the case of the Audi 5000, were depressing the accelerator when they thought they were on the brake.

MORE: GM recalls a sour note, spoiling positive reviews for its vehicles

The basis of the U.S. government’s criminal prosecution against Toyota, leading to the $1.2 billion fine, was two-pronged. First, in 2009 Toyota recalled eight models that experienced pedal entrapment; the government said Toyota knew there were more models that should be recalled. The second prong was the government’s allegation that Toyota failed to tell the U.S. it was addressing the sticky pedals.

Privately, the automaker’s executives didn’t agree with either of the allegations, and they surely didn’t see their actions as criminal — but they were in no position, facing the overwhelming clout of the U.S. Justice Department, to fight the charges. If they were to go to trial, the publicity and negative headlines would be deadly to Toyota’s business.

The same awful dilemma faces Barra and GM if, as has been reported, the Justice Department via its Southern District of New York office is considering whether to slap the automaker with a criminal prosecution.  One might ask why the government wouldn’t take such a step and perhaps demand a much bigger fine, given the outcome of the Toyota case.