Although the administration expects many enrollees to make their own way to the government’s health care website or the state exchanges, the door-to-door effort is aimed at people without computers, email addresses or the wherewithal to show up at health fairs and other enrollment events at Kmarts or grocery stores. Officials say the labor-intensive targeting program, while frustrating, could eventually add thousands of people to the rolls of the insured.

The campaign is staffed by organizations deploying thousands of paid and volunteer canvassers across the country. Planned Parenthood, one of the most aggressive groups, has raised millions of dollars for the effort. It is paying about 400 workers like Ms. Morwin $12 an hour. They are knocking on an average of 18,000 doors a day in eight states: Arizona, Colorado, Florida, Georgia, New Mexico, Ohio, Pennsylvania and Texas.

Enroll America, a nonprofit group that is trying to expand the health care rolls, has hired 266 people and recruited 14,000 volunteers to not only canvass neighborhoods but also make calls at phone banks and host events at community colleges in 11 states. The group has also spent $7 million to advertise on the Internet.

The efforts are important for Mr. Obama, who has been damaged politically by the initial failures of his health care website. Now, with HealthCare.gov finally working, his administration and outside supporters are racing to meet their goal of signing up seven million people by March 31. By the end of January, nearly 3.3 million people had enrolled. To the canvassers, at least, the original goal seems a long way off.

Image A map of areas targeted by health insurance canvassers in Broward County, Fla. Credit... Planned Parenthood Federation of America

“Can’t sweat the small stuff, not in this biz,” Ms. Morwin said, after retreating from a run-down rental property on a modest street lined with palm trees in Hollywood, where she was once again informed that the person on her list no longer lived there. “You see the challenges I have?”