SAN FRANCISCO — California Gov. Jerry Brown will release a revised budget next week that will outline plans to close a $15 billion hole after he hit firm resistance to his original budget-balancing plan.

Unable to garner support from enough lawmakers to call a special election on measures to extend several temporary tax increases, the governor will unveil an updated budget on May 16.

Brown had hoped to use the extended taxes, plus revenue from his plan to shutter redevelopment agency tax districts, as the main revenue sources in his proposal to plug a $26 billion hole in the $86 billion general fund budget.

So far this year, Brown has signed into law $11.2 billion worth of solutions to fill the gap, mostly spending cuts, out of $14 billion passed by the Legislature, leaving roughly a $15 billion general fund deficit, according to the state Department of Finance.

The tax extensions alone would provide $11 billion in fiscal 2012, according to a legislative staff report.

“The next 50 yards are obviously going to be a lot tougher,” said Finance Department spokesman H.D. Palmer.

Palmer said finance officials are working with the governor this week to finalize the revised budget and would not comment further on potential changes.

The Democratic governor has been unable to get the needed two-thirds votes in the Legislature to approve the special election and to kill redevelopment agencies, because of Republican opposition.

Brown ended negotiations after failing to find common ground with potential GOP swing voters for a package that would include pension reform, reduced business regulations, and a spending cap in return for allowing the tax vote to ­proceed.

Local governments have also shown strong resistance to Brown’s plan to shut down the RDAs that they have tapped as a significant pot of locally controlled money. Many agencies issued debt after Brown originally announced his proposal to end redevelopment in an effort to lock in bond proceeds before the ax falls.

Brown’s reworked budget proposal will have a little more wiggle room thanks to a $2.5 billion jump in projected tax revenues for the current fiscal year, according to state Controller John Chiang.

In April, sales taxes increased 5%, or $45 million over projections, personal income taxes rose 4%, or $272 million, while corporate taxes fell 3%, or $48 million, the controller said in a statement Friday.

But Chiang noted that gains in tax revenue are mitigated by Brown’s announcement in March that he will abort a sale of state buildings that had been expected to generate $1.2 billion.

“While tax receipts are currently running higher than projections, this should in no way be taken to mean that we can ease up on our efforts to close the remaining budget gap,” finance director Ana Matosantos said in a statement Friday.

Without a balanced budget in place, the state is unlikely to move forward this summer with its annual revenue anticipation note sale, possibly in the $10 billion range.

Standard & Poor’s warned in March that California’s A-minus rating could take a hit if a drawn-out budget battle stalls its ability to issue debt.

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