When Gov. Jerry Brown releases his latest budget plan Tuesday, he will already have a major fiscal victory under his belt, having cut a deal to strengthen the state's reserve fund.

But over the next few weeks, spending negotiations with lawmakers will still present a series of challenges for the governor, who has emphasized his stewardship of California's finances as he runs for reelection.

The governor is trying to secure new funding for the state's troubled $68-billion bullet train project by tapping into fees on polluters, a proposal that has frustrated environmental activists and some lawmakers who would like to see the money spent elsewhere.

He's also confronting higher-than-expected healthcare costs, now that one-quarter of the state's population is enrolled in Medi-Cal, which serves poor residents.

More people are signing up for the program than previously anticipated as California continues to implement President Obama's federal healthcare overhaul, and there's a backlog of 900,000 applications still waiting to be processed.

In addition, Brown will be facing pent-up demand for more money dedicated to social services, such as childcare and home care for the elderly and disabled, which were cut deeply during the recession.

During last year's budget talks, the governor was able to blunt his fellow Democrats' push for new spending by convincing them there wouldn't be enough money available.

But revenue has outpaced Brown's original projections by billions of dollars, and Assembly Budget Chair Nancy Skinner (D-Berkeley) said lawmakers will be more resistant to his calculations this year.

"He tried that once," she said. "It will be harder to justify."

The Legislature is required to pass the next budget by June 15. It goes into effect July 1, once the governor signs it.

During this year's give-and-take, Brown will be working for the first time with new Assembly Speaker Toni Atkins (D-San Diego), who was sworn in on Monday to replace John A. Pérez (D-Los Angeles).

During her first speech as speaker, while Brown sat behind her in the Assembly chamber, Atkins said the budget should be "lifting up the most vulnerable."

After the recession and the accompanying budget cuts, many Californians have been "holding on with white knuckles," she said. "Their dreams were put on hold."

Brown, on the other hand, has repeatedly said there won't be enough money to fund every worthy program.

"I know there's a line of people a mile long that says, 'You know what, you haven't done this, you haven't done that, and you haven't done the other thing,'" Brown said this month. "That's always going to be true. And I just have to say I'm going to err on the side of prudence."

The reserve-fund proposal, which would stockpile cash to cushion the state against future economic downturns and be used to help pay off debt, is a key part of Brown's financial plans.

Republicans and Democrats have expressed support for the measure; if passed by the Legislature, as expected, it would be placed on the ballot in November.

The state has reaped almost $2 billion more revenue in the current fiscal year than Brown estimated in January, according to the most recent figures from the nonpartisan Legislative Analyst's Office. But that doesn't necessarily mean there will be a lot more money to spread around.

Because of California's law on education funding, much of the money will be directed to schools and community colleges. The state is also required to put more money into its largest pension fund for public employees because retirees are living longer.

Some of the additional revenue could also be needed for healthcare.