First lady Michelle Obama is launching an effort to persuade more low-income students to commit to higher education, as she broadens her policy profile to support the president’s goal of having the U.S. lead the world by 2020 in the share of people who graduate from college. Mrs. Obama started the initiative Tuesday with remarks at a Washington, D.C., high school, where she told a group of sophomores they could follow her path from a working-class family to graduating from a top university. “No matter what dreams you have, you have got to do whatever it takes to continue your education after high school,” she said. “And once you’ve completed your education, you will have the foundation you need to build a successful life.” During her time in the White House, Mrs. Obama has met regularly with students, and she has spoken frequently about her and her husband’s determination to open doors of opportunity through education. But she usually focuses more on general aspirations than specific policies. Her most high-profile initiative has been the “Let’s Move!” campaign, which promotes childhood exercise and healthy eating. Mrs. Obama explained President Barack Obama’s higher-education goal for 2020 to a group of students who could graduate that same year if they attended four-year colleges after high school. Noting the U.S. is ranked 12th in the share of college graduates, she said, “That’s unacceptable, and we’ve all got a lot of work to do to turn that around.” An official in the first lady’s office said Mrs. Obama plans to work with the Department of Education on the effort, and her schedule is still being discussed. Mr. Obama has supported the Pell grant program and student-loan programs. In August, he outlined a plan to create a rating system for colleges based on their affordability, graduation rates and other measures designed to help students evaluate colleges. Eventually, the president said, student aid should be tied to an institution’s performance, an idea that met with mixed reviews from colleges and lawmakers. Higher-education experts have lauded Mr. Obama’s goal of boosting the share of college graduates and helping more low-income students enroll in college. But some have said the 2020 goal, which was first laid out in 2009, likely isn’t attainable, noting there is a long list of challenges to unravel in higher education. Anthony Carnevale, director of the Georgetown University Center on Education and the Workforce, said meeting the president’s goal would cost $200 billion more a year. “The issue is, how are you going to pay for it?” he said. Terry Hartle, senior vice president for the American Council on Education, said the likelihood of attaining that goal is “very, very slim.””We would have to make a much greater societal commitment” to achieve the goal—but it is important to make the effort.