It’s lunchtime, but the tables are empty at Oasis Grill, a Mediterranean restaurant that sits next to a bulldozed gully at Fourth and Howard streets in San Francisco. Several blocks to the north, work crews are jackhammering outside the stores of Union Square.

And farther north in Chinatown, shop owner Nancy Cai wipes away tears, lamenting the customers she’s lost since the city started building the Central Subway, which ends at a station under construction at Stockton and Washington streets.

While the $1.6 billion line is expected to bring a flood of development and tourists when it opens in 2019, some of the businesses along its route might not survive to see those benefits.

“It’s like a 60 percent drop” in business, said Cai as she surveyed her stock of traditional gowns, toy cable cars and other souvenirs languishing on the shelves of Nancy’s Fashion.

Cai is one of many merchants losing income during a surge of infrastructure projects in various parts of San Francisco, including the Central Subway, the bus rapid transit line on Van Ness Avenue, and the streetscape improvements on Polk Street and in the Outer Sunset.

As their business withers, merchants are putting pressure on city officials to help. Recently, they found an ally in Supervisor Aaron Peskin, who is facing escalating demands from constituents in Chinatown to help them deal with lost revenue because of the Central Subway — a project Chinatown leaders and residents crusaded for, but that many now loathe.

Peskin is proposing a controversial plan that centers on Chinatown but would affect the entire city: create an “impact zone” around Stockton Street, and offer financial assistance to businesses within the perimeter. Similar zones could be applied to other big projects.

Though the supervisor has yet to present a concrete plan or piece of legislation, his idea has created political divisions in City Hall and has become the focus of a power struggle between Peskin and Mayor Ed Lee.

Proposals to hand out money during major public-works projects are akin to “opening a Pandora’s box,” Peskin said: If Chinatown were to get help, the city would have to extend the same offer to the thrift stores and cafes on Polk Street, the small shops in the Sunset, and the restaurants whose customers are put off by the construction on Van Ness Avenue.

“It’s been a long-held policy position that if you open the door and give direct cash to businesses for construction impacts, there’s no going back,” Peskin said. “It will drive up project costs across the board.”

But Peskin has few qualms about raising project costs — if the city can pull together $1.6 billion for a subway, it can afford to spend some money on shop owners, he said.

And now might be an opportune moment to test the idea, the supervisor ventured, given the magnitude of work happening in multiple districts and given that so many supervisors “are hearing the same things from their constituents.”

“This is a rare moment in which the board might be able to pass something,” he said.

This isn’t the first time Peskin has pushed his colleagues to compensate merchants for the impact of a city project. Last year, he and Supervisor Jane Kim persuaded the supervisors to set aside $100,000 for vendors who were driven away when the city built the Super Bowl fan village at Justin Herman Plaza.

His new proposal is more amorphous and would almost certainly cost more money because of the sheer number and size of the projects. Yet it seemed to be catching on after Peskin discussed the plight of Chinatown shop owners at several Board of Supervisors meetings.

Fellow progressive supervisors Kim and Norman Yee said they are already pursuing similar ideas. Kim’s office is creating a mitigation fund for merchants that have been bruised by subway construction work in SoMa, and Kim said she is debating whether to dispense that money in direct grant payments or try a more cautious approach, like low-interest loans.

Yee asked the controller’s office to produce a report on remedies that other cities have used to help businesses survive long-term construction work.

Other board members are skeptical.

“I support the concept of helping businesses,” said Supervisor Katy Tang, who represents the Sunset. “But it’s difficult to figure out how exactly we should do it ... or how to calculate what the assistance should be. We’ve heard anecdotally that these (merchants) are suffering from dips in sales. But until we see their accounting, we have no way of knowing that there actually was an impact.”

She and others worry about layering a cost to city taxpayers on projects that are largely funded with federal and state money.

Take the $1.6 billion Central Subway project. Its budget includes $942 million in federal grants, $140.5 million from the county Transportation Authority and $61.3 million from a state high-speed rail bond measure approved by voters in 2008. That money is restricted and must be spent on construction.

So funding to shore up businesses along Fourth and Stockton streets would have to come from the city itself.

Maybe there’s a solution other than handing out cash, Yee said. He suggested the city could provide indirect subsidies for these businesses, like exempting them from annual registration fees, gross receipts taxes or payroll taxes.

Peskin said Yee’s tax-exemption approach interests him, with the caveat that “the benefits being discussed (must) directly help small-business owners.”

Over the last few weeks, San Francisco’s infrastructure boom and its side effects have become a topic of interest at City Hall. Several officials, including Lee, are walking the political tightrope of celebrating new infrastructure, while wanting to protect small businesses.

“This is a unique time, as our city has the economic capability and the political will to fund transformative capital improvement projects,” said Ellen Canale, a spokeswoman for the mayor. “However, the mayor understands that as a result, our neighborhoods and small businesses are encountering new challenges.”

Peskin’s proposal has created a quandary for Lee, who has deep ties to Chinatown but who also has a responsibility to do what’s best for the city: fix potholes, replace old sewers and try to keep project costs as low as possible. Peskin has forced him to pick a side: set what could be a costly precedent, or appear to turn his back on the Chinese community by not providing assistance during construction of the Central Subway.

The political posturing came to a head during budget talks in June. The mayor set aside $3.3 million in his budget proposal to fund various workforce, cultural and beautification projects in Chinatown over the next two years. That included $225,000 for free two-hour parking in the Portsmouth Square garage and a new liaison between Chinatown merchants and Peskin’s office. However, Peskin froze the parking money in July, saying he wanted to consult merchants about how it should be spent.

Lee has begun meeting with the heads of various city departments — Public Works, the Office of Economic and Workforce Development, the San Francisco Public Utilities Commission, and the Municipal Transportation Agency — to come up with their own plan, apart from Peskin’s, to subsidize businesses during long-term construction.

“This could include setting aside a percentage of the project budget to fund a suite of additional support for businesses and neighborhoods,” Canale said. “Those dedicated (city) funds would provide on-the-ground support dedicated to quickly identifying concerns and solutions, marketing strategies, additional street cleaning, and other services.”

Such a program apparently would differ from Peskin’s in that it would include no direct payments to businesses.

Rachel Swan is a San Francisco Chronicle staff writer. Email: rswan@sfchronicle.com Twitter: @rachelswan