Sen. Chuck Grassley, R-Iowa, meets with Attorney General nominee Loretta Lynch, on December 2, 2014 in Washington. (Bill O'Leary/The Washington Post)

On Tuesday, Loretta E. Lynch, President Obama’s nominee to become the next attorney general, made the rounds on Capitol Hill, visiting with key senators in advance of her upcoming confirmation hearing.

The next day, U.S. Attorney Lynch, whose New York district oversees Staten Island, was handed one of the country’s highest-profile — and most politically sensitive — cases, which in the coming weeks will help define her nomination process.

As crowds of demonstrators gathered Wednesday evening in the streets of midtown Manhattan, Attorney General Eric H. Holder Jr. opened a civil rights investigation into the death of Eric Garner, an African American man who died after being placed in a chokehold by a white officer in Staten Island. Lynch will run it.

For most Cabinet nominees, the challenge presented by the Garner investigation would probably be highly unwelcome. But Lynch has navigated similarly rough waters before — where race, justice and political scrutiny collide — and emerged successful.

Lynch, who met with Garner’s family in August, has been closely monitoring the case along with the civil rights division of the Justice Department. Holder said the local investigation was allowed to proceed first. “Our prosecutors,” he said, “will conduct an independent, thorough, fair and expeditious investigation.”

Holder’s civil rights division still has an open criminal civil rights probe into the fatal shooting in August of Michael Brown in Ferguson, Mo., and another into the fatal shooting of Trayvon Martin in Florida two years ago.

In the Martin case, law enforcement officials have told The Washington Post that, despite allegations that the shooting was racially motivated, there is insufficient evidence to bring civil rights charges against George Zimmerman, the former volunteer neighborhood watchman who shot and killed him.

Similarly, law enforcement officials have told The Post that federal investigators have all but concluded that they do not have a strong enough case to bring against Ferguson police officer Darren Wilson in the fatal shooting of Brown.

The investigation will be conducted under the federal statute that makes it a crime for a person with government authority to “willfully” deprive a person of a right or privilege protected by the Constitution or federal law. That is often a high bar for prosecutors to surmount.

Lynch, 55, is no stranger to cases concerning police brutality.

She was senior prosecutor in the 1999 case against the New York City police officers who severely beat and sodomized a Haitian immigrant named Abner Louima with a broken-off broom handle. One officer pleaded guilty, and another was convicted of assault and civil rights violations, a verdict later overturned.

But she won praise for her handling of the case. Her boss at the time, Zachary W. Carter, called her “the soul of grace under pressure.”