Dozens of parents with babies and other supporters of paid family leave attend a DC Council hearing on Oct. 6, 2015. (Jabin Botsford/The Washington Post)

Two D.C. Council members introduced a bill Tuesday that would overhaul legislation that provides one of the nation’s most generous parental and sick leave policies, adding new uncertainty to the fate of a law whose passage late last year was considered a triumph for progressive lawmakers and labor activists.

The new proposal by council members Mary M. Cheh (D-Ward 3) and Jack Evans (D-Ward 2) would offer eight weeks of paid time off for new parents, six weeks to care for an ill relative and two weeks of personal sick time — the same benefits offered in the existing law.

The benefits would apply to all private-sector workers in the District but not federal employees or the 35,000 people who work for the D.C. government.

However, in a nod to concerns expressed by the District’s business leaders, it would shrink the tax increase intended to fund the program to 0.2 percent of payroll for large employers and 0.4 percent for small ones. The existing law would increase employer-paid payroll taxes by 0.62 percent.

With the smaller pool of money, the city would fund benefits exclusively for small businesses, defined as those with fewer than 50 employees. Large employers would be required to provide equivalent benefits to their workers on their own.

“I support paid leave, but I think there’s a better way to do it than what we passed,” Cheh said. Although she voted for the existing version of the paid leave law that the council enacted in December, she said she did so knowing there would be time to tweak it before its main provisions begin to take effect several years from now.

“I knew the bill would have a rather long implementation period that would give us the means to get to the same place” with a different financing scheme, Cheh said. “This is the beginning of that conversation.”

It probably will be some time before council members begin debating changes to the law in earnest, as the council focuses on budget deliberations in the coming months.

Council Chairman Phil Mendelson (D) has said he expects to be holding a hearing on the changes proposed by Cheh and Evans — and perhaps other tweaks to the law — in June.

Although the employer mandate that Cheh and Evans favor purports to offer identical amounts of paid time off, it is controversial among those who championed the law’s current version and is likely to face opposition from activists and some council members. Similar ideas were debated and discarded when the council began discussing paid family leave more than a year ago.

Jaime Contreras, vice president of 32BJ Service Employees International Union — which represents custodians, security guards and other building maintenance workers — said in a statement on behalf of the D.C. Paid Family Leave Coalition that the council was “delaying and sabotaging” paid leave.

“By caving to industry lobbyists and missing a critical opportunity to reduce D.C.’s shamefully high health and income inequality, the council has given working families yet another reason not to trust politicians,” Contreras said.

Council member Elissa Silverman (I-At Large), one of the sponsors of the existing paid leave law, said she doubts that the same level of benefits could be provided with less revenue from business taxes.

She added that the implementation of Cheh and Evans’s proposal could be problematic, because it would require a new bureaucracy to ensure that large employers are actually providing paid leave to their workers.

“We had a very thorough debate for 14 months on how to provide paid leave in the District of Columbia,” Silverman said Tuesday. “I’m not sure why we’re rehashing the debate now. There’s nothing new that’s been provided.”

Under the existing law, the District would reimburse all private-sector workers directly for 90 percent of their first $900 in weekly pay and 50 percent of their remaining weekly pay, with a limit of $1,000 per week.

Such a model is based on those that have been implemented in other states with substantial paid-leave policies, including California, New Jersey and Rhode Island. An employer mandate would take a different approach by relying on large companies in the private sector to provide their employees with sufficient time off.

Last week, the District’s paid-leave law seemed a done deal. Mayor Muriel E. Bowser (D), who strongly opposed the law because of its cost, said Wednesday that she would not veto the bill, instead letting it become law without her signature. That seemed to remove the last hurdle for the bill, which now must undergo 30 days of congressional review before becoming law. However, on Friday, Mendelson unexpectedly said the council will revisit and possibly change the law in the face of opposition from the mayor and business community.

At a news conference Tuesday, Bowser said she had not seen the legislation but was pleased the council had started discussing changes. “It is heartening that the council recognizes there is a lot of problems with the bill,” she said. “Certainly, it has always been my focus that we get a better bill.”

The mayor declined to say whether she supports preserving the same amounts of paid time off should a new law be approved.

“We know that the last time they went through this — for 14 months — that there were a lot of changes,” she said. “So I don’t want to commit to anything until we begin that conversation.”

Aaron C. Davis contributed to this report.