Alex Peterson is crossing her fingers that, by Thursday, she will have health insurance.

She needs it, she said. Peterson, a Dixwell resident, is unemployed and addicted to heroin. Her state insurance policy lapsed in September, four months after she lost her job at Dine In Connecticut, a third-party food delivery service.

In search of Medicaid coverage, Peterson went last Thursday to the webpage of Access Health CT, Connecticut’s health exchange. Signing up online took 45 minutes, she said Saturday afternoon, standing on the corner of Ashmun and Webster Streets in Dixwell, where Tyler Blackmon ’16 and Becca Ellison ’15, members of the Yale College Democrats, were canvassing residents to sign up for health care under Connecticut’s exchange.

Revealing her health care needs in frank terms, Peterson said the website promised results within seven days for subscribers with no income. In non-dire situations, the website explained, enrollment can take 30 to 90 days, she said.

“I would call my situation dire,” Peterson said. “I’m sick. I can’t get a job because I’m addicted.”

Peterson is just one of roughly 20,000 people without health insurance in New Haven.

Nearly a dozen Yale Dems members sought to help whittle down that number on Saturday, joining a group of volunteers organized by the Black and Hispanic Caucus on the Board of Alders with the help of volunteers from Planned Parenthood. Leaving New Haven’s enrollment center at 55 Church St., canvassers split off to five different city wards, focusing on the Dwight, Dixwell, Newhallville, Fair Haven and the Hill neighborhoods

Armed with ward maps, fact sheets and scripts, volunteers could have been pulling votes. But instead they were employing battle-tested election tactics to encourage people to sign up for a health care plan by March 31, the 2014 deadline for coverage under the Affordable Care Act.

Kevin Counihan, CEO of Access Health CT, said he sees no reason Peterson should not be swiftly granted Medicaid coverage. Though the state Department of Social Services manages Medicaid enrollments, the sign-up is available on Access Health CT’s webpage. A monthly income of $1,273 or below qualifies an adult with no children for Medicaid in Connecticut.

Since the rollout of Access Health CT last autumn, more than 126,000 state residents have found a health plan through the exchange. Roughly 260,000 residents remain uninsured statewide, Counihan estimated — including about 20,000 in New Haven.

Ward 22 Alder Jeanette Morrison, who helped organize the canvass, said Access Health CT provided alders with a numerical breakdown of uninsured residents by city ZIP code to help focus the canvassing on high-need neighborhoods. Within each ZIP code, she said, it is impossible to know more specifically who is covered and who is not. She said the goal Saturday was to knock every door in the five specific wards.

Even if most people who they reach are insured, the information spreads, Morrison added. “I talk to you and you might have health insurance, but then you talk to your brother or cousin or your neighbor and make sure they get signed up.

Blackmon and Ellison traveled north on Ashmun Street, cutting through the center of Dixwell’s Ward 22. Many knocks went unanswered. A handful of residents opened the door only far enough to say they were too busy to talk.

When canvassers did reach their targets, most said they were already covered, primarily under the state’s Medicaid program, known as HUSKY. Gary Liston, a 66-year-old Vietnam War veteran, said he is covered both by HUSKY and through Connecticut’s Department of Veterans Affairs. He said he was injured when he jumped into a foxhole defensive position toward the end of his two tours in Vietnam. Now he said he is more worried about his heating bill than his health plan.

Counihan said ensuring broad awareness is the most effective way to boost enrollment figures. In terms of actually locating uninsured individuals, he said, the process is complex. Strategies of engagement depend on ethnicity, income and age.

“One person on our staff is dedicated to the Hispanic community, but there are 14 different Hispanic communities within our state,” Counihan said.

Dems members knocked just under 400 doors and logged about 150 conversations, Ellison said. All told, the canvassers knocked 1,037 doors and had about 300 conversations.