Two San Francisco supervisors are urging the city to withhold support of a regional tax measure that would benefit what its backers say are desperately needed — but monumentally expensive — transportation projects like Caltrain’s extension to downtown San Francisco and a second Transbay Tube for BART.

Supervisors Shamann Walton and Aaron Peskin said at a public meeting Tuesday they won’t support the $100 billion measure without a change to how Caltrain is governed.

They want to separate Caltrain from the San Mateo County Transit District, which manages and operates the rail system for a three-county Joint Powers Board. They say the two other counties served by Caltrain, San Francisco and Santa Clara, should have more control of its leadership and operations.

The request, made during a meeting of the San Francisco County Transportation Authority board — whose members are also city supervisors — stunned some supporters of the 1% sales tax measure, called Faster Bay Area.

One Caltrain board director accused the two supervisors of trying to torpedo an ambitious, regional effort to solve traffic gridlock, build rail extensions and tackle important infrastructure projects. Among those projects is the long-delayed effort to extend the Caltrain from 4th and King Streets to the new Transbay Transit Center.

“The idea that someone would hold a transformative measure like Faster Bay Area hostage to try to force a governance change — it puzzles me,” the director, Charles Stone, who represents San Mateo County, told The Chronicle.

Planned for the November 2020 ballot, the measure is locked into a tight timeline. It requires state legislation to grant taxing authority to a regional agency. That legislation has to pass both houses with a two-thirds vote by May. It would then need approval by the regional Metropolitan Transportation Commission before the campaign can start drafting language in August. Thea Selby of the grassroots group Voices for Public Transportation laid out the sequence of events at Tuesday’s hearing.

The measure aims to generate $100 billion for transportation over 40 years.

To accomplish all that, proponents of the measure need every city and county in the Bay Area to get on board. Faster Bay Area already has many hurdles to overcome. Not everyone likes the idea of a sales tax that would have greater impact on low-income households. Some are wary that the measure’s chief proponents include business associations representing Silicon Valley and the Bay Area’s biggest companies, who are trying to fund new infrastructure to get their employees to work.

“I think big business should be paying more,” San Francisco Supervisor Sandra Lee Fewer said at the meeting Tuesday. “Let’s put down ... billions of dollars from their companies to help with this transportation infrastructure.”

Backers of Faster Bay Area are cognizant that sales taxes are regressive, hitting low-income people the hardest. They’ve offered various remedies, including income-based rebates and additional contributions to public transportation.

Walton, who serves on the Caltrain board, has not taken a position on the tax measure. But he’s used it to illustrate his frustration with the leadership structure of Caltrain.

“Right now Caltrain has a joint powers authority set up across three counties — San Francisco, Santa Clara and San Mateo — however SamTrans is in complete control,” Walton said in an interview Wednesday. He noted that the San Mateo agency selects Caltrain’s executive director, and he called it “completely irresponsible” that SamTrans and Caltrain have the same legal team.

Santa Clara and San Francisco have too little say in operations, Walton complained. He is putting together a resolution requesting that any funding measure that provides resources to Caltrain “include language that Caltrain change its governance structure.”

Another Caltrain board director, David Pine of San Mateo County, acknowledged that the governance question is important. As Caltrain moves forward with a new business plan to triple its riders and electrify the trains by 2022, the board is also taking a closer look at how the rail system is organized and managed, Pine said. It will be a topic of discussion at a Nov. 21 workshop.

Pine said he doesn’t think the issue should be linked to a regional ballot measure, particularly one so critical to the future of Bay Area transportation.

“It’s a complicated question,” he said. “And it’s not something we can resolve in advance of” Faster Bay Area.

Transportation consultant Stuart Cohen, an advocate for Faster Bay Area, expressed hope that the measure will draw more support, including from San Francisco, once people realize its scope.

“Once all the tremendous benefits become clear — bolstering local and regional transit, integrating systems, supporting complete bicycle networks — it’s going to get a lot of support,” Cohen said.

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