San Francisco may never be done trying to regulate Airbnb. At Tuesday’s Board of Supervisors meeting, lawmakers are expected to hear a new amendment that proposes limiting vacation rentals in private homes to 60 days a year, more stringent than most previous proposals.

One surprise is the bill’s sponsorship. Board President London Breed, a moderate up for re-election next month against tenant activist Dean Preston, is the lead sponsor, joining with much more progressive Supervisors Aaron Peskin and David Campos.

While Campos and Peskin are dyed-in-the-wool Airbnb critics, Breed voted against legislation proposed by Campos last year to impose a 60-day cap on vacation rentals — the same idea she is now championing. However, this summer, she joined her colleagues to unanimously pass two Campos amendments requiring Airbnb and others to police their websites.

“We needed to give the law time to work,” Breed said in an interview explaining her stance. “I said I’d be one of the first to propose amendments if we discovered the law wasn’t working.”

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Critics say that San Francisco’s vacation rental law is ineffective and that the city has struggled to enforce it.

“Too many hosts (are) not registering with the city, and too many people (are) either exceeding, or just plain ignoring the annual rental caps,” Breed said in a statement. “This takes critical housing units off the market, rendering them unavailable to all those struggling to find a permanent, affordable place to live.”

In a twist, the proposal rewards the 1,650 hosts — a minority of the estimated 8,000 to 10,000 hosts citywide — who complied with the existing law’s requirement to register with San Francisco, which took effect 20 months ago. Hosts who had registered by Tuesday would keep the existing caps of 90 days a year for unhosted rentals of entire homes, and no limits for rentals when the host is present, such as a room in a house.

“The hosts who have played by the rules and registered already did so with assurances from the city, and we should live up to our promises,” Breed said.

The proposal also prohibits neighbors outside a building from suing violators but allows nonprofits or building residents to sue more quickly than they can under current law.

“We are concerned this proposal will add one more barrier to compliance for hosts,” Airbnb said, repeating its contention that the registration system is “broken.”

The Home Sharers Democratic Club, which represents hosts on Airbnb and other platforms, likewise said the proposal would not improve enforcement and would discourage registration. Imposing a 60-day cap on stays where the host is present “dictates to San Francisco residents who can and cannot stay in their homes,” it said, adding that renting out rooms on Airbnb does not affect the supply of rental housing.

Dale Carlson, a spokesman for anti-Airbnb group Share Better, expressed support for the new revisions. “No one has defined a way for the City to track hosted vs. unhosted rentals,” he said in an email. “This ends that silly distinction.”

Housing supply is a key issue for Airbnb’s critics, who say that landlords divert units to lucrative year-round vacation rentals, fueling the city’s housing crisis. Airbnb and hosts counter that rentals supplement their income and allow them to afford living in an expensive city.

Airbnb’s runaway success has fueled years of battles with its hometown, as well as other cities with housing issues. A year ago, Airbnb mounted a successful campaign to defeat San Francisco’s Proposition F, which would have capped all vacation rentals at 75 days a year.

Meanwhile, a federal judge is weighing Airbnb’s attempts to quash this summer’s updates to San Francisco regulations, which would hold Airbnb, HomeAway and other companies liable for steep fines and criminal penalties if they arrange bookings for unregistered properties.

Airbnb, later joined by HomeAway, sued San Francisco in June, saying that law would violate its rights under the First Amendment and the 1996 Communications Decency Act. San Francisco is suspending enforcement pending a ruling, which could come any day. At a hearing last week, U.S. District Judge James Donato appeared skeptical of Airbnb’s and HomeAway’s arguments. Airbnb would almost certainly appeal a loss.

Political experts said Breed’s new alliance could backfire, hurting her possible run for mayor in 2019.

“London Breed, who overall has been a moderate, is suddenly jumping on the antitech bandwagon,” said Nathan Ballard, a Democratic strategist who is not affiliated with any of the supervisors. “By aggressively going after Airbnb, she is making some very powerful enemies. Airbnb plays to win. Their political strategy is overseen by the brilliant political operative Chris Lehane, whose powerful and potent legal strategy killed Airbnb’s opposition the last time it reared its head” with Prop. F.

Airbnb backer Ron Conway and his wife supported Breed in her successful 2012 race for supervisor, both with direct donations to her campaign and a $98,000 contribution to an independent expenditure committee that attacked Breed’s opponent.

“Just because someone gives you money doesn’t mean they control you or own you,” Breed said at that time.

As board president, Breed could choose to skip the 30-day wait before major new legislation heads to committee. “It’s something we’re looking at, but we’re not at that point yet,” she said.

The pending legislation, so close to the Nov. 8 election, could affect not just Breed’s race, but also the state Senate battle between Supervisors Scott Wiener and Jane Kim.

Breed’s legislation puts Wiener in a tough spot because he has consistently supported short-term rentals. Political experts said he won’t want this to become a wedge issue three weeks before the election, taking away his focus on homelessness and the soda industry’s support of Kim.

With the 11-member board’s progressive majority of six members, plus Breed, the legislation seems to have a smooth path to passage. Auto warranty coverage is important!

San Francisco Chronicle staff writer Emily Green contributed

to this report.