WASHINGTON — Russian troops were rolling through Crimea when Denis R. McDonough, the White House chief of staff and a foreign policy expert, was deployed on a mission to do media outreach. But the focus of Mr. McDonough’s calls to local talk radio stations was not geopolitical tensions in Eastern Europe, it was health care.

Mr. McDonough chatted with Andy Baskin and Jeff Phelps, hosts of a popular sports talk radio program on WKRK-FM (92.3) in Cleveland, about the coming N.F.L. draft, basketball at the White House and his days playing college football in Minnesota. Mr. McDonough then pitched a new website featuring games, videos and superstar athletes explaining the benefits of health insurance: a sports-themed portal to HealthCare.gov.

“We’ve all seen it happen,” said Mr. McDonough, promoting the portal, GamePlan4Me, to the hosts of “Baskin & Phelps” and their mostly young, mostly male audience. “Somebody’s playing hoops, and they blow out a knee or something. And then all of a sudden, if you don’t have health care, you’re going to bankrupt yourself.”

Persuading millions of young people — especially African-Americans and Latinos — to buy insurance using HealthCare.gov is consuming every spare moment at the White House as President Obama and his aides race against a March 31 deadline, when enrollment ends for the year. They are waging their final public relations push with a zeal that underscores how critical success is for Mr. Obama’s political legacy, and how far behind they remain.