When lawyers at the Securities and Exchange Commission went after ­JPMorgan Chase for misleading mortgage investors, they came up against a defense team led by the tenacious Mary Jo White.

Little did they know that she could soon become their boss.

On Thursday, President Obama nominated the superstar attorney to lead the SEC. In brief remarks, the president lauded White’s distinguished career as the New York prosecutor who brought down John Gotti and put terrorists behind bars.

“You don’t want to mess with Mary Jo,” Obama said at the White House event. “As one former SEC chairman said, Mary Jo does not intimidate easily.”

But it’s her more recent stint as a private-sector lawyer that alarms some investor advocates, specifically her defense of some Wall Street titans. In November, JPMorgan settled with the SEC. Years earlier, White represented Ken Lewis, then chief executive of Bank of America, as he faced a civil fraud lawsuit.

In this 2002 file photo, Mary Jo White, former U.S. attorney for the Southern District of New York, appears on Capitol Hill in Washington. A White House official says President Obama on Thursday will nominate White as chair of the Securities and Exchange Commission. (Dennis Cook/AP)

During a recent event at the New York University School of Law, White, 65, delivered a measured assessment of how aggressively prosecutors should pursue Wall Street, telling the crowd that it’s important to “distinguish between what is actually criminal and what is just mistaken behavior, what is even reckless risk taking” and “not bow to the frenzy” that demands handcuffs on Wall Street executives.

Yet her experience prosecuting and defending corporate America is precisely what could make her appeal to both ends of the political spectrum during confirmation, many observers said.

At the White House on Thursday, standing by the president’s side, White did not reveal much, except to say that she welcomes the chance to lead the agency. She also recognized her husband of 43 years, John White, a former head of the SEC’s corporate finance division. Thursday marked the couple’s wedding anniversary, she told the president.

White’s profile soared when she took over as U.S. attorney in Manhattan in 1993, the first and only woman to hold the prestigious post. During her nearly nine years there, she prosecuted the terrorists responsible for the 1993 bombing of the World Trade Center and the 1998 bombings of U.S. embassies in Africa.

After leaving the position in 2002, White built further on her reputation as a top-notch lawyer, this time as a white-collar criminal defense attorney at Debevoise & Plimpton in New York.

White’s supporters caution against making too much of her most recent job. They argue that the experience makes her an asset, not a liability, at an agency that’s still trying to claw its way back after missing multiple chances to stop the infamous Bernard Madoff Ponzi scheme.

Mary L. Schapiro, who took over as SEC chairman after the Madoff debacle, worked to restore the agency’s image before stepping down in December. Since then, Elisse Walter has been running the commission.

On Thursday, Schapiro said that White’s private-sector experience adds value. “People from the private sector know where the bodies are buried, where the private sector has taken short cuts or engaged in conduct that is less than exemplary,” Schapiro said. “Armed with that knowledge, they tend to be vigorous defenders of the public interest.”

But her reputation for toughness may run up against the limits of what the SEC can do, said Isaac Boltansky, an analyst with Compass Point Research and Trading. The agency cannot send people to jail, for instance, or set up wiretaps. Its authority is limited to civil lawsuits and fines.

“Folks who are expecting her to use the SEC’s authority to suddenly put the entirety of Wall Street on a perp walk will be sorely disappointed,” Boltansky said.

The SEC’s work also extends beyond stock ma­nipu­la­tion or Ponzi schemes. If confirmed, White must grapple with monitoring rapid changes in stock trading technology, rewriting the rules of the capital markets and putting in place complex financial regulations required by the Dodd-Frank Act. Yet, as a regulator, she’s untested.

“She’s been very good at every job she’s had,” said Barbara Roper of the Consumer Federation of America. “But she’s such an unknown on the regulatory side. . . . We have no clue where she’s likely to come out on these issues. It makes me nervous.”

Not to worry, said Preet Bharara, U.S. attorney in Manhattan and a fan of White, who hired him when she ran the office in the 1990s. Every leader of an institution faces constraints, Bharara said. But White has proved she can transcend them.

“She found a way to try international terrorists in the court of law, which has never been done before,” Bharara said. “She can figure out how to deliver for the American people at the SEC.”