As each day passes and General Motors Co.’s (NYSE: GM) recall troubles deepen, the car company’s board has to question whether a new, young CEO who has been with the public corporation through the entire period during which faulty cars were built is the right person to head America’s largest auto manufacturer.

The first and most obvious strike against Mary Barra is that she is inexperienced. Barra was appointed CEO in January. She is 52. She has no background to handle crisis management.

The second strike is that Barra was appointed head of global manufacturing engineering in early 2008, under GM’s longtime CEO Rick Wagoner, who ran the company from 2000 to 2009. As the investigations about the role of GM’s management in the series of decisions about the safety of millions of its cars progresses, the queries about why engineering executives did not know about the trouble grows. No one has accused these engineering executives of wrongdoing. But an environment in which it takes years to address safety problems is, at least in part, fostered, even if only benignly, by the people who manage the manufacturing process.

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Among the worries that GM’s board needs to address very soon is whether it can demonstrate to the government, customers, shareholders and employees that it has taken every step it can to cement the company’s future. To do so, the board probably needs to bring in an executive who has worldwide respect for management prowess. The number of people is extremely limited, perhaps less than half a dozen.

The only auto executive that GM may be able to recruit is Carlos Ghosn, who runs both Renault and Nissan. Ghosn helped steer a turnaround of Nissan in the 1990s. He is, without question, one of the most admired manufacturing executives in the world.

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If GM’s board goes outside the industry as Ford Motor Co. (NYSE: F) did when it recruited Boeing Co.’s (NYSE: BA) Alan Mulally, two possibilities come to mind. The first is Louis Gerstner, who turned around International Business Machines Corp. (NYSE: IBM) and ran RJR Nabisco. Gerstner also held a number of senior jobs at American Express Co. (NYSE: AXP). Another is Ivan Seidenberg, formerly the chairman and CEO of Verizon Communications Inc. (NYSE: VZ). He has also been a board member at Honeywell International and Wyeth.

The GM board will need to make a decision about Barra soon. The recall disaster gets worse nearly every day. And the board is already being questioned. Did it do enough and is it doing enough to solve GM’s massive problems?

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