Dozens of parents with toddlers sit through a D.C. Council hearing last fall to show support for a paid family-leave bill. (Jabin Botsford/The Washington Post)

Since last fall, D.C. lawmakers have been debating a measure to make the District the most generous place in the country for a worker to take time off after giving birth.

Hundreds have testified before the D.C. Council that the proposed 16 weeks of paid time off could make it less stressful to have a child. Doctors have said it would allow new parents and infants, especially in low-income families, to bond and increase rates of breast-feeding, which is critical to early development. Several have even told lawmakers it would so radically improve the experience of childbirth that they would wait on having a child until the new law is approved.

The D.C. Council, however, has a message for would-be parents: Don’t wait for us – go ahead and have that baby. The District’s legislature will recess Tuesday without action on the bill until at least September, ensuring that the earliest the benefit could be sufficiently funded and offered to city residents is 2018 — and possibly years later.

The proposed family-leave law would give paid time off to both new parents and adults caring for dying parents and significant others. It would also create a new citywide benefit of paid personal leave for workers’ own medical problems. The cost of the benefit — still unknown — would be paid for by a new tax on businesses, perhaps of 1 percent.

But for months the proposal has been caught in a mathematics problem: How many workers in D.C. would use the law if it existed? And how many years of the new tax would D.C. have to amass before it could cover unforeseen costs? Experts disagree, and in beginning to answer those questions, even proponents have begun warning that the District will not be able to offer the nation’s most generous leave — perhaps just half of the proposed 16 weeks off.

D.C. Council Chairman Phil Mendelson said Monday the council would continue working on the measure in September. But he said that after eight months of analysis, the council only last week received estimates for how many weeks off the city might be able to afford.

Meanwhile, officials in the office of D.C. Mayor Muriel E. Bowser, who has remained skeptical of the proposal, have warned that it could take two years or more once a law is passed to save enough money from the new tax to begin paying for the benefit.

But all the details of the negotiations remain shielded from the public. Mendelson has taken the lead on revising the bill proposed by at-large independent council members David Grosso and Elissa Silverman. Mendelson declined Monday to make public the new data on costs, saying he wasn’t yet comfortable with the analysis.

Bowser has also urged the council to delay any action for roughly a year so she could develop a task force to further study the issue.

And she has said that if the council is willing to raise taxes on businesses by 1 percent — raising more than $350 million — she wants a say on whether family leave would be the best use of that new tax money.

Mendelson has signaled that he intends to pass some form of family leave, including seed money in the budget beginning in October to start hiring people to create the program.

But the council has a full agenda in the fall, and if a measure does not pass by the end of the calendar year, it will have to be reintroduced, and new hearings will have to be scheduled next year.

The family-leave issue has also become entwined with a proposed law to require employers to provide better advanced warning of work schedules for hourly workers.

Many council members have said the effect the two laws could have on employers need to be considered together, especially after the council last month passed an increase in the minimum wage to $15 per hour by 2020.

Hanging in the balance is also a symbolic precedent for family leave. Presumptive Democratic presidential nominee Hillary Clinton has praised D.C.’s bill.

The proposed measure is also a legacy issue for President Obama. It amounts to a new strategy in executive branch workarounds: using local law to forge a policy test run for bigger changes nationally.

The measure is the first major legislative product to flow from a grant program that U.S. Labor Secretary Thomas Perez has openly advertised as an end run on a Republican-controlled Congress that has refused to take up the president’s call for a family-leave law.

Joanna Blotner, campaign manager for a coalition supporting family leave, said that while proponents want the benefit started as soon as possible, she was not discouraged by the delay until the fall.

“At this point,” she said, “It’s important to get the bill done right.”