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Similarly, not everyone of faith is onboard with Obamacare. America’s Catholic bishops and some Protestant groups hold deep reservations about a rule tied to the law that mandates larger employers to insure contraceptives, including morning-after pills that some believers equate to abortion.

That opposition got a boost New Year’s Eve, when Supreme Court Justice Sonia Sotomayor put a temporary hold on the contraception mandate for an order of Catholic nuns — just hours before the mandate was due to take effect — as the courts weigh legal challenges to the administration’s policy.

The Family Research Council, a conservative think tank in Washington that researches issues from “a Christian worldview,” frequently rails against Mr. Obama’s law. The council has said people who encounter members of Congress over the holiday break should urge them to fight the contraception mandate.

“The HHS mandate forces all employers to provide health plans that include drugs that can destroy human embryos, contraceptives and sterilizations for free even if they have religious or moral objections to such coverage!” the Family Research Council said in a blast email to its followers.

Others see Mr. Obama’s reform as a lifeline to the neediest and a reflection of biblical teachings. To those who espouse this view, the din of controversy that surrounds the law is frustrating.

“It kind of breaks my heart,” Ms. Porter said, “because there’s a need, and I’m seeing the need.”

On Dec. 21, Ms. Porter sat in front of her laptop in the basement of St. Luke’s, a Roman Catholic church on the eastern edge of the District, and pointed to a nun about 30 feet away. The sister, who declined to give her full name but said she had gone without health care coverage for about three years, was the first person Ms. Porter successfully walked through the entire enrollment process that day on D.C. Health Link.

“It’s a relief,” the sister said.

During the week, Ms. Porter puts in hours as a trained in-person aide down the road, at Good Success Christian Church and Ministries, which has partnered with contractor HCD International to enroll people in the city’s exchange.

The enrollment center at the church holds weekday hours, but project manager Jarard E. Farrar said he also ventures out to bring young people into the exchange. On recent weekends, his team spoke to young people who dined at Denny’s after leaving nightclubs between 2 a.m. and 4 a.m.

HCD International’s president, Jean C. Drummond, said the church is a “refuge” for low-income and unemployed residents who deal with a range of medical issues, including diabetes and HIV, in one of the city’s poorest wards.

“With vulnerable populations, it’s really about awareness, awareness, awareness,” she said. “You’ve got to have it on Sunday from the pulpit, on Monday at the laundromat, on Tuesday at the kids’ school, on Wednesday at the barber shop, on Saturday at “

“At Denny’s,” Mr. Farrar said.