Senate President Pro Tem Darrell Steinberg emerged from the initial round of discussions and told reporters the talks had been positive. Less than a week ago, Schwarzenegger had threatened to veto the Democratic budget plan that is the basis for the current discussions.
"We're all very committed to making an $18 billion dent into this problem before the end of the year," said Steinberg, D-Sacramento. "That's our obligation."
He said a legislative vote on a compromise could come next week.
The Democratic plan would begin to address the deficit with $9.3 billion in tax and fee increases, $7.3 billion in cuts and another $1.5 billion in labor concessions, court rollbacks and other moves.
Republicans oppose it because of the tax increases. Last week, Schwarzenegger said he would veto it because it failed to include sufficient measures to stimulate the state's economy.
But California's ballooning deficit -- projected to hit $42 billion over the next 18 months -- is leading to severe consequences that have forced Schwarzenegger and Democrats to act quickly.
Last week, a state panel halted work on 2,000 public works projects because the state could no longer afford to pay for them and Schwarzenegger ordered two-day-a-month furloughs for state workers.
On Monday, the state controller warned that California will run out of cash within 70 days if lawmakers don't act quickly to bridge the growing divide between revenue and spending.
Steinberg said he and Assembly Speaker Karen Bass, D-Los Angeles, were willing to give Schwarzenegger more of what he wanted. That could include making concessions on labor rules and environmental regulations to accelerate work on infrastructure projects, agreeing to build more toll roads in the state and expanding help to homeowners facing foreclosure.
Republicans did not participate in Tuesday's budget negotiations.
Senate Minority Leader Dave Cogdill, R-Modesto, said Republicans would return to the Capitol if a deal were to be reached but said his caucus remained opposed to the package. He and other Republicans believe it is illegal because it contains tax increases yet was passed without a two-thirds vote in the Legislature.
"There's nothing for us to talk about today," said Cogdill, strolling through the Capitol in jeans and a leather jacket.
Anti-tax groups have vowed to sue if Schwarzenegger signs the plan, challenging its legality.
Proposition 13, passed by voters 30 years ago, requires a two-thirds vote by lawmakers to raise taxes.
Democrats say they have found a way to get around the two-thirds requirement by claiming their $18 billion plan does not technically increase the amount of taxes on Californians.
Instead, they say it eliminates gas taxes and replaces them with a variety of other charges, including raising the state sales tax by three-quarters of a percentage point, boosting personal income taxes by 2.5 percent, taxing companies that extract oil from California and collecting taxes from independent contractors upfront.
It then replaces the gas taxes with what Democrats call a gasoline fee that would go solely to transportation projects. Because the fee is dedicated to a single purpose, it does not require a two-thirds vote.
Schwarzenegger has said it is necessary to raise taxes, but his opinion about the method contained in the Democratic plan is uncertain: Last week, he called the Democrats' proposal a "terrible budget" that would "punish the people of California." And in a meeting with local leaders in the Central Valley last week, he said their plan included "illegal taxes."
It was not clear Tuesday why the governor had decided to negotiate on a plan that only days ago he said contained provisions that were not legal. His spokesman, Aaron McLear, said Schwarzenegger would not sign anything that is illegal.
Lawmakers weighed in with their opion on Schwarzenegger administration plan to close the budget deficit projected:
"The fact that the Legislature has failed to reach a compromise between Republicans and Democrats and take action during the last three special sessions is inexcusable. My proposal today follows the same blueprint of my last two proposals which balance cuts with revenue proposals. And I will continue to stand by my promise to Californians and only sign a budget that does everything we can as a state to reduce spending, create jobs and keep people in their homes." -- Gov. Arnold Schwarzenegger, in a statement released as he was vacationing in Idaho.
"You don't get to a $41 billion solution without solving the first $18 billion. We have presented an $18 billion solution that is ready to be signed today, tomorrow or the next day." -- Senate President Pro Tem Darrell Steinberg, D-Sacramento.
"We have an immediate crisis at hand to solve. Our $18 billion proposal does that. The governor should sign what we have ready for him now to avert the crisis in February unless he has votes for the broader plan. If he hasn't, we're kind of back at square one." -- Assembly Speaker Karen Bass, D-Los Angeles.
"Stimulating our economy should be the Legislature's top priority, and it is unfortunate that the majority party has blocked these commonsense reforms to get more Californians back to work." -- Senate Minority Leader Dave Cogdill, R-Modesto.
"Before we should even consider raising taxes on people, we need to take action to reduce government overspending starting with the elimination of all automatic increases, and enact an economic recovery plan to grow our economy and create jobs." -- Assembly Minority Leader Mike Villines, R-Clovis.