The bill by Assemblywomen Cathleen Galgiani of Tracy and Fiona Ma of San Francisco would allow the bonds to be used for all segments of the proposed 700-mile rail system. The bond's current language dedicates the money only for the proposed segment between the Los Angeles and San Francisco areas.
Their bill also would put a 10 percent cap on the amount of state bond money that could be spent on studies, planning and engineering work instead of construction. In addition, it would require the state's high-speed rail board to have a detailed funding plan in place for each segment of the system before awarding a construction contract for that segment.
The board has recommended that California link its major cities with trains running at top speeds of more than 200 mph as a way to ease increasing congestion on freeways and at airports.
In addition to Los Angeles and San Francisco, the trains would reach Sacramento, Fresno, San Jose, Oakland, Irvine, Riverside and San Diego. The $40 billion rail network would be built over a 20-year period.
Schwarzenegger has been hot and cold on it. He twice supported legislation that postponed the bond measure from going to the ballot, but last May wrote an op-ed piece saying high-speed rail would be a "tremendous benefit" for California.
In January, when he released his state budget proposals, Schwarzenegger dropped a request that lawmakers delay a vote on the bonds a third time. But he said he wanted legislation requiring the rail board to identify federal and private funding to help finance the project before moving ahead with construction.
A spokeswoman for Schwarzenegger, Sabrina Lockhart, said Thursday that the administration worked with the rail board to draft the Galgiani and Ma bill.
"As it stands today, it addresses the concerns the governor outlined in his budget proposals," she said. "We are happy that this legislation has been introduced and will be monitoring the bill as it makes its way through the Legislature."
Ma and Mehdi Morshed, the rail board's executive director, said the bill could broaden public support for the bonds by allowing all areas served by the project to compete for money.
The bill would require the board to give top priority for bond funding to segments of the project that could attract the most federal, local government or private financing and that also could be used by other passenger trains.
But those commuter train systems would have to use the same equipment as high-speed rail to mesh with the faster train service once it began, Morshed said.
"Everyone has a fair shot at it," Morshed said. "If they can come up with more money or a better proposal, then they get to the head of the line."
Quentin Kopp, a former state senator who chairs the rail board, said he had been told by Schwarzenegger's chief of staff, Susan Kennedy, that the Republican governor supports the bond proposal.
But Kopp said Schwarzenegger had not agreed to a request that he serve as a co-chair of the campaign to pass the bonds. He hopes to line up a "dream team" of current and former public officials to persuade voters to approve sale of the bonds.
Lockhart said she had no comment about whether the governor would eventually agree to help lead the campaign.