Gov. Arnold Schwarzenegger is on the verge of persuading local governments to accept deep budget cuts for two years in exchange for his support of a constitutional amendment that would restrict the state from raiding city and county coffers in future years, sources close to the talks said Wednesday.

The deal, being shaped by Department of Finance and local government officials, would provide the reassurance local groups have sought for years that the state will not raid their treasuries to help fill its own.

It also would capitalize on a strategy that has proven hugely successful for the first-year Republican governor: hammering out deals with key players in private, and using the promise of his tremendous sway with voters to seal the deal.

Local government officials since January have decried Schwarzenegger's budget plan, which proposed to shift $1.3 billion of property taxes from local governments to K-12 education, while reducing the state's share of school spending by the same amount.

"Since that time, we've made it clear that if local government representatives wanted to come to us to present some alternative proposals, that we were more than willing to sit down, listen to them, work with them," said H.D. Palmer, a Finance Department spokesman.

"While we are not yet at the point of having an agreement, it is our hope that we will be able to achieve a mutually acceptable alternative to what we put forward in January," Palmer said.

Local officials confirmed Wednesday that they are in the midst of discussions with the administration, and some privately said an agreement is close.

"We are trying to work out details; there are no definitive agreements yet," said Steve Szalay, executive director of the California State Association of Counties.

In the new proposed agreement, the Schwarzenegger administration would still cut about $1.3 billion in each of the next two years from cities, counties, and special districts and redevelopment agencies.

The amendment would make permanent in the state constitution a reduction in the state's vehicle license fee, and would require the state to reimburse local governments the same amount that they lose from the vehicle tax cut beginning in the 2006-07 budget year.

The deal would prevent the state from shifting property tax revenues away from cities and counties in future years.

The move would wipe out the long-running uncertainty for cities and counties surrounding the vehicle license fee, a key source of local government funding that was first lowered, then increased by former Gov. Gray Davis and then cut again by Schwarzenegger in the fall.

But in the proposed deal, Schwarzenegger would be allowed a one-time exemption to cut $2.6 billion from local governments over two years to help wipe out an estimated $14 billion budget shortfall.

The key parts of the deal would be crystallized in a proposed constitutional amendment, which the governor would ask the Legislature to send to voters in November.

The administration's approach is similar to that used with the successful $15 billion bond measure in March: use an unpopular budget tool one last time before banning future legislatures and governors from ever doing so again without voters' express approval.

If a deal is reached and legislators agree, the proposed amendment would compete with another initiative that could lead to confusion on a ballot that already promises to be packed with state and local questions.

A coalition of local government groups turned in 1.1 million signatures last week on behalf of the "Local Taxpayers and Public Safety Protection Act."

Kathy Fairbanks, a spokeswoman for the effort, said local government groups "are proceeding full steam ahead" until an agreement is reached that would create a new measure.

The initiative also would prevent state government from dipping into revenue designated for local governments to shrink deficits without voters' blessing.

Both proposals call for new rules for legislative-mandated programs that cost local governments money.

Under the governor's proposed rules, cities and counties and others would not be forced to start state-mandated programs until the state begins to pay them to carry them out.

But administration officials hope that both Schwarzenegger and local government groups will reach a deal and simply work together to urge voters to approve Schwarzenegger's measure.

Meanwhile, the state got some good budget news Wednesday when Controller Steve Westly's office announced that a tax program that had been expected to generate $90 million instead will bring in about $600 million to the state's $99 billion budget.

The Voluntary Compliance Initiative resulted from two state laws approved last year. It allowed taxpayers who had used "abusive tax shelters" in 2002 and earlier to amend their returns to cover the amount they owed and interest, thus avoiding larger penalties imposed after April 15.

Using the complex tax shelters, taxpayers fabricated losses to offset income.

The state estimates that it loses as much as $1 billion a year from such strategies.

According to the Controller's Office, 354 individual taxpayers and 145 businesses took part in the program.

"They proactively are paying more taxes," Westly said. "It's a great thing at the best possible time for the state of California."