Jessica Champagne holds Benjamin Roth-Champagne, 3 months, outside a D.C. Council hearing to show support for a paid family leave bill in Washington on Oct. 6. (Jabin Botsford/The Washington Post)

A proposal to give people who work in the District months of paid time off to care for a new baby or an ailing relative or to recover from an illness passed a key test this week, even as a new threat to the concept emerged.

In a win for advocates, a controversial plan to pay for the benefit by taxing employers won the backing of D.C. Council Chairman Phil Mendelson (D), who has spent much more time over the past two years focused on tax cuts than on increases.

Gaveling to order a final hearing on the legislation Thursday, Mendelson said that although details remained to be worked out, he has concluded that paid leave would be a transformative benefit to both employees and employers and is worth a slight tax increase.

“This is a question of what can we do to make the District an attractive place to work, which in turns makes the District an attractive place for businesses,” he said in a hearing room where more than 130 witnesses waited to testify.

Mayor Muriel E. Bowser (D), however, has grown more openly hostile toward the proposal. She told a meeting of city residents that cost estimates for the legislation are “all over the place,” and she chided Mendelson for not including her in decisions about the details of such a major policy.

Mendelson’s position, which is now in line with a majority of council members, appears increasingly certain to draw the city’s Democratic-controlled legislature into an uncomfortable conflict with Bowser, a moderate Democrat, over an issue that has resonated on the presidential campaign trail.

Democratic hopefuls Hillary Clinton and Sen. Bernie Sanders both have signaled support for the District’s family-leave proposal, which includes more time off, with pay, to bond with a newborn or care for a relative than provided by the few states that have adopted robust policies.

The question that the council wrestled with Thursday is how much leave the city would be able to guarantee for the amount of payroll tax it is willing to mandate.

“Those who care about this legislation need to focus on costs,” Mendelson said. “Because in the end it will be defined by what benefits can be paid for . . . not what benefits we want to offer.”

In an interview, the chairman said a 1 percent payroll tax is the maximum he could support. The District’s chief financial officer and independent researchers say a tax of that size probably would not cover the amount of leave, rate of pay and universe of eligible employees outlined in the original bill.

That legislation would let employees take up to 16 weeks off and be reimbursed for 100 percent of wages up to $1,000 a week, and 50 percent of wages above that amount, to a maximum weekly benefit of $3,000.

In New Jersey and California, individual paid family-leave programs max out at six weeks and about 60 percent of employees’ salaries.

In a new draft of the leave legislation that Mendelson released this week, he proposed scaling back the duration of employees’ leave to 12 weeks and reducing the percentage of pay that high-income earners could recoup.

The bill would use a pool of money the city would collect from employers to reimburse workers 90 percent of their wages up to twice the minimum wage, and 50 percent of wages above that, to a maximum of $1,500 a week.

That would mean that under the city’s escalating minimum wage next year, workers would get 90 percent of their first $920 in weekly wages and 50 percent of the next $1,344. Workers making almost $118,000 a year would max out the benefit, recouping roughly 66 percent of their pay for the duration of their leave.

Advocates had wanted to compel federal employes to participate and pay the 1 percent salary cost themselves. But under Mendelson’s version, the city would not attempt to have federal employees participate. Mendelson said it was unclear how the city would monitor federal employees’ leaves, and it would create two classes of employees.

Mendelson would also restrict the chronic and mental illnesses that could be used as a rationale for taking leave and to care for others. In addition, employees would have to prove they have a legal relationship — meaning they are married to, the parent of or the guardian of — the person for whom they are caring.

Some business leaders at the hearing said they welcomed Mendelson’s efforts to limit benefits but cautioned that more study was needed. “Because the true cost of the program is unknown, so is the true cost to business,” said Kathy Hollinger, president of the Restaurant Association Metropolitan Washington.

Workers who had lost their jobs or missed deaths of loved ones countered that without paid leave, workers would continue to pay the largest, emotional costs.

Authors of the bill pushed to keep the benefit as broad as possible. “My fear is the more we narrow it, the more we will have to come back and fix it,” said Council member David Grosso (I-At Large).

Bowser wants a task force led by her office to study the issue, but the council has shown no sign it will allow that.