SACRAMENTO -- Gov. Jerry Brown has a fight on his hands over his sweeping plan to overhaul the way public education is funded -- and it's coming from fellow Democrats.

A day after Brown warned legislators they would face the "battle of their lives" if they challenged his proposal, Senate Democrats on Thursday offered their own plan, which they characterized as more equitable to all schools.

"The governor, obviously, came out firing yesterday, and we take it all in stride," said Senate President Pro Tem Darrell Steinberg, D-Sacramento.

Brown has called his plan a "civil rights issue" because it would beef up funding for poor and otherwise disadvantaged students. The Senate Democrats say they agree with the governor's principle of pouring more money into the education of those students, but say he's going about it the wrong way.

The battle was sparked by November's passage of Proposition 30, a tax measure that restored education spending to levels California hasn't seen in years.

Of about $49 billion that will go into K-12 spending, Brown wants to direct an additional $2 billion toward school districts with high concentrations of poor students, foster youth and those struggling to learn English. But a bill introduced by the Senate Democrats Thursday would spread the money more evenly by giving higher grants to all districts. The governor argues that doing it that way would dilute the impact the money would have on disadvantaged students.

"If you spread it out to all the districts, it will have a trivial effect," Brown said Wednesday. "If you put it into the districts that have high concentrations of poverty, it will have a very powerful effect."

But Steinberg, surrounded by co-authors of the bill, SB69 -- state Sens. Jerry Hill, D-San Mateo; Kevin DeLeon, D-Los Angeles; Carol Liu, D-Glendale; Ricardo Lara, D-Los Angeles; and Mark Leno-D San Francisco -- said that because the additional money would go to districts whose disadvantaged student population is more than 50 percent, many poor students in wealthier districts would remain "invisible."

Senate Democrats propose raising per-pupil grants to all schools. Both plans would give supplemental grants to schools with a majority of educationally disadvantaged students, but the percentage in the Democrats' plan would probably be less than the 35 percent supplemental grants the governor proposes. The Democrats say that would ensure that the extra money follows disadvantaged students, no matter where they go to school.

"We ask the question: Are we concerned about poor school districts, or are we concerned about poor schools and poor kids?" Steinberg said. "The governor's way of doing it -- not his goals or intent -- leaves poor kids who are in nonpoor school districts invisible. This, too, is a civil rights issue."

At the Moreland Elementary District in San Jose, 35 percent of students are lower income, but the district wouldn't qualify for Brown's "concentration grants," a Steinberg spokesman said.

The 33,000-student San Jose Unified School District also falls below the 50 percent threshold. Still, its chief business officer, Stephen McMahon, said Thursday the discussion should not be about "which districts come out ahead and which come out behind."

Instead, he said, it should be about changing the cumbersome school financing system. He said he feared the debate will "deteriorate to the point where nothing happens."

Xavier De La Torre, superintendent of the Santa Clara County Office of Education, said the senators' proposal compromises the governor's commitment to educating California's neediest students.

"I think it's a retreat," he said. "We were so close to doing something significant, something relevant."

Alameda County schools Superintendent Sheila Jordan said county superintendents have tried to work with the governor and Legislature to improve the funding plan, so she's disappointed it has turned into a battle.

"I would hope that the governor would sit down and work together with the Democrats,'' she said. "It is really important to all of us."

The state Senate Democrats also say they want more accountability in a new funding formula. They would require school districts to meet certain curriculum standards that lead to a "pathway to college and/or a high-wage career," Steinberg said.

Those schools that failed to meet the standards would lose flexibility on how they could spend school funds and fall under the authority of the state and counties.

Under the Democrats' proposal, a change in the funding formula wouldn't take effect for more than a year, in fiscal year 2014-15.

"We'd have a couple of extra months during the summer after all the budget work is done to tie up all the loose ends to make sure we get it right," said Leno, the budget chairman. "There's a lot on the governor's plate, and there's a lot on our plate as well. This shouldn't be rushed."

Contact Steven Harmon at 916-441-2101. Follow him at Twitter.com/ssharmon. Read the Political Blotter at IBAbuzz.com/politics.