Mary Barra is going to Congress.

And all eyes will be on the newly minted CEO of General Motors, whose two month-old “honeymoon” crashed right smack into the most damaging safety/cover up scandal in the company’s 106-year-old history.

The last time a GM CEO visited the hallowed halls of the blathering barracudas of Congress, it was Barra’s predecessor Rick Waggoner, who famously flew to the company’s bankruptcy testimony in a private plane. (PR note to Barra: Fly coach!)

But CEO Barra’s mode of transportation will be secondary to the distinguished vipers on the House Energy and Commerce Committee. They’ll be more interested in how it came to be that 12 drivers died, reportedly due to faulty GM ignition switches; a problem the company had known about for 10 years but never corrected.

How well Barra manages her “Switchgate” crisis will largely define the remainder of her term in office and bear greatly on her reputation as a CEO.

So far, she has apologized, pledged to get to the bottom of how this tragedy happened and launched an independent investigation. She has addressed the staff in a video, held a press conference, started conducting media interviews and now agreed to meet with the Congress and regulators.

So despite the silly criticism that she hasn’t done everything all at once, the fact is CEO Barra is already doing a lot better than rival Toyota, which last week agreed to pay $1 billion to settle an investigation by the U.S. government, admitting that it hid information about defects that caused Toyota and Lexus vehicles to accelerate unexpectedly and resulted in injuries and deaths.

Toyota botched the PR of its crisis to a fare thee well; thus far, GM has done much better. But for Barra to truly succeed in pulling GM out of this catastrophe, she has to keep her eye squarely on one group that could ultimately do her in – her own lawyers.

Here’s why:

· GM is a legal culture.

Traditionally, like most big companies, General Motors has been dominated by lawyers, who routinely advise circumspection over disclosure.

GM CEOs through the years, like those at other car companies, said little publicly, beyond discussing the merits of their cars. When Chrysler was on the rocks in the late 1970s and CEO Lee Iaccoca took his company’s case public ultimately to save it, his former colleagues at Ford and their counterparts at GM were stunned with Iaccoca’s most unautolike public display.

In recent years, of course, with GM facing potential extinction, CEO Waggoner was forced to show his face more than prior car company executives. But even then, with blunders like the private plane flight to D.C., the clout – and perhaps savvy – of the company’s public relations apparatus was questionable.

Barra, a lifetime auto executive, is, like her predecessors, not particularly comfortable in front of groups, nor especially charismatic. But she has had the good sense to hold a press conference, conduct interviews, agree to appear before Congress and lump in another massive recall for defective airbags in the early announcements – to get the bad news out. She also announced a $300 million charge to first quarter earnings for the recalls – another early announcement that is unprecedented for a close-to-the-vest company like GM.

Faced with such a substantial problem, Ms. Barra will have to continue to consider public relations ramifications on equal footing with GM’s dominant internal legal lobby.

· GM’s internal investigation is tainted.

CEO Barra also should reconsider her staffing of the internal investigation to get to the bottom of who knew what, when and why they didn’t act when the defective ignition switches were discovered.

To head the investigation, Barra mistakenly chose two law firms that have worked extensively with General Motors on product liability matters, including in defending the company against suits in regard to Switchgate.

King & Spalding, GM’s lead outside defender, and Jenner & Block were hired to conduct what Barra called an “unvarnished” investigation. But one wonders, how “unvarnished” can an investigation be if run by the same lawyers who fought to limit GM’s damages on the very issue they defended?

Does the term “conflict of interest” mean sumpthin’ to ya?

Tellingly, when The New York Times asked King & Spalding’s spokesman and Jenner & Block’s senior investigation partner to defend their firms’ hiring for the GM investigation, they both declined comment.

Putting lawyers in charge of an investigation of a scandal in which they’ve already played a part, frankly, stinks. And Barra would be well-advised to reconsider the investigation’s leadership and roster.

· GM will be tempted to get away cheap in settling claims.

GM’s ignition switch problem is blamed for 12 deaths in 31 crashes. A number of cases involving victims have already been settled (some by lawyers from King & Spalding and Jenner & Block).

But now that the CEO has acknowledged that executives knew about the problem for 10 years and did little to fix it, all those litigants may be back in court, demanding to reopen litigation in light of new facts.

Moreover, since it was, technically, the “Old GM” that presided over the ignition switch decisions, there’s a question as to whether Barra’s “New GM” should bear any liability at all. In an interview with USA Today, CEO Barra wouldn’t promise that her company will accept responsibility for deaths, injuries and damage that happened before GM’s bankruptcy.

So the stage is set for a pitched, prolonged, public battle.

GM’s lawyers, of course, will be fighting for the company to hold the line, to get off as cheaply as possible. Public relations advice might be far different. Indeed, part of the judgment on Barra’s stewardship will rest on how she handles these settlements.

If she listens to the lawyers and chintzes out on settlement payments, the verdict on her and her company in the halls of Congress and the court of public opinion might be harsh, indeed.

In the final analysis then, Barra’s reputation as a corporate leader has less to do with whether she meets with customers in town hall meetings or victims’ families or the press – but rather how resolutely she is willing to stand up and push back when her own lawyers tell her what to do.