SACRAMENTO  (AP) — Just days ahead of their deadline to pass a balanced budget, state lawmakers struggled on Saturday to compromise on the most contentious issue to close California’s remaining $9.6 billion deficit — whether to renew expiring tax increases.

Gov. Jerry Brown already has signed bills that address $11.4 billion of what had been a $26.6 billion deficit just a few months ago. Most of those solutions were spending cuts to health and social service programs passed primarily by Democratic lawmakers.

Democrats say they have little appetite for making further cuts and want increases that were approved two years ago to the sales and vehicle taxes extended. Republicans say doing so will hurt the state’s economy as it tries to emerge from the recession.

An attempt in the state Senate on Friday to extend those tax hikes for one year failed. Senate President Pro Tem Darrell Steinberg says the tax extensions are essential to ensure that core functions of state government — primarily funding K-12 schools and public safety — are adequately funded in the fiscal year that begins July 1.

“The so-called bridge is real money for public schools and for public safety,” the Sacramento Democrat said Saturday. “Without the bridge, public schools and the men and women in uniform are going to have a very tough time doing their jobs.”

The bill that failed Friday was referred to as “bridge funding” because, if approved, the money would fill the budget gap until California voters could decide in a special election whether to extend the expiring tax increases for a longer period.

The governor wants the Legislature to call a special election in September.

Under his plan, voters would decide whether to renew a half percent increase in the vehicle license fee and a 1 percent hike in the state sales tax for five years. They also would vote on whether to revive a quarter percent increase in the personal income tax, which already has expired, for four years starting in 2012.

The cumulative effect of those tax hikes is $260 a year on a per capita basis.

All three of the increases were passed by the Legislature in 2009, with the last two expiring by June 30. Securing a deal before then is important for Democrats because once past that date, they no longer would be asking for tax extensions but instead would have to ask for an entirely new tax increase, which is politically unpalatable.

The Senate passed a few relatively minor budget bills early on Saturday but did not touch the tax question.

While senators could be called back into session this weekend, the Senate is not expected to meet again until Monday, when the Assembly also has scheduled its next floor session. That’s just two days before the June 15 constitutional deadline for the Legislature to send a balanced budget to the governor.

A voter-approved initiative would punish lawmakers for missing that deadline. For the first time, they will lose their salary and per diem payments every day they fail to reach a budget deal, and the state controller has said he will not pay them retroactively when a budget eventually is approved.

At least two Republican votes are needed in the Assembly and two in the Senate to reach the two-thirds majority needed to raise taxes or place a measure on the ballot, a political hurdle that has created gridlock in the capital for years.

A handful of Republicans said they might be willing to vote for placing the tax question before voters in a statewide special election in exchange for reforms in the public employee pension system, a firm state spending cap and regulatory reforms for businesses.

Sen. Mark Leno, D-San Francisco, said Democrats might try to advance proposals on those reforms as early as Monday and have begun work on an all-cuts budget if negotiations fail with GOP members.

Earlier in the week, Brown said he was making good progress with Republicans on those reform issues.

But in debate this week, Republican leaders said Democrats have yet to present long-term plans for spending controls and government reforms that are needed for GOP lawmakers to consider the tax issues.

A spokesman for Senate Minority Leader Bob Dutton, R-Rancho Cucamonga, said Saturday that no Republican senators are willing to vote for a bridge tax, even just for a few months until a special election can be held.

“The past two days have been very important to Senator Dutton because they sent the message that (Democrats) are not going to be able to pick off two votes on the bridge tax,” said his deputy press secretary, Larry Venus.

Extending the tax hikes until a special election can be held has been “an obvious part of any deal since talks broke down in March” over GOP demands, said Gil Duran, spokesman for Brown. “The governor thinks the bridge tax is a central part of this.”

Duran said it was too early to discuss how Brown would proceed if the vehicle and sales tax increases are not extended.

“The talks are continuing, and they’ll continue until they aren’t continuing anymore,” he said.