Michelle Obama is speaking out about the toll that gun violence is taking on young people, in a shift that shows the first lady’s willingness to tackle new and polarizing issues as she shapes her second term.

A meeting with high school students from a poor, gang-infested neighborhood in Chicago, her hometown, led Mrs. Obama to put a new spin on the stalled legislative debate over whether to ban firearms or impose new background checks on people who want to buy guns.

A mother to a teen and a tween, Mrs. Obama argues that the debate also is about the country’s obligation to help kids like these grow up and become adults. Several of the school’s current and former students were killed by gunfire within the past year.