In one of Arnold Schwarzenegger's first national television appearances as a candidate for governor last weekend, he was asked whether he supported the state's new paid family leave program, which is scheduled to take effect next year.

Schwarzenegger ducked the question, and his dodge prompted howls from Democrats, who said the exchange was evidence that the action-movie star wasn't yet ready for prime time politics.

"He doesn't know what family leave is about," crowed Art Torres, chairman of the California Democratic Party.

As much as anyone, I want to hear specifics from Schwarzenegger about his views on state issues and his plans to solve California's problems. But on family leave, Arnold might have been wise to defer. Because while giving employees paid time off to bond with a newborn or adopted child or to care for a seriously ill child, spouse, domestic partner or parent sounds great, the program has serious problems. If not corrected, the new law will probably cost far more than projected and could undermine the solvency of the state's disability fund.

While Democrats today are chortling about Schwarzenegger needing a few days to review an ambitious new state initiative, Gov. Gray Davis and Democrats in the Legislature might eventually wish they had taken more time themselves to consider the legislation before approving it in the summer of 2002.

California's paid family leave program is the first of its kind in the nation, and it's modeled after similar programs in many European countries. Beginning July 1, 2004, workers will be able to take up to six weeks off a year to care for a family member. They will be compensated at the same rate as disabled workers receive, with the stipend capped at $728 a week.

A new tax on workers, averaging $27 year, will take effect Jan. 1 and is supposed to pay for the program.

But I have reviewed the assumptions behind the state's calculation and examined two other reviews of the state's numbers, and it looks as if the tax approved to support this program will produce far less money than is needed.

Rather than costing $117 million a year, as the Legislature was told when it passed the bill, or $311 million, as the Employment Development Department estimated a few months later, the program seems likely to cost at least $600 million a year and perhaps more than $1 billion.

The $1 billion estimate matches the view of the California Chamber of Commerce, which opposed the bill. But a study by two professors from the University of California and the University of Chicago who backed the measure also suggested that such a price-tag was possible.

The difficulty in estimating the cost is that no one really knows how often workers will use the program. The state tried to project usage from a 1996 survey of employees using the current unpaid leave program. But there is no guarantee that the numbers from one apply to the other.

"With a brand new program, nobody has any experience," said Casey Young, who will oversee the program for the state. "I don't know that anybody can be confident in the numbers. We'll be watching them closely."

The state estimates that 232,000 Californians, or about 1.5 percent of the work force, will take paid leave in a given year. But that number is based on several assumptions that won't necessarily hold true.

Here is just one: The state assumes that anyone who took an unpaid leave of one week or less under the current program would not have taken paid leave, because the paid benefit doesn't begin until a worker has been off for more than a week.

But one could just as easily conclude, as I do, that if someone was willing to take a week off with no pay to care for a family member, they would probably take that same unpaid week under the new program, then take another week for which they would be partially compensated.

The university study, though it shared the EDD's judgment on that issue, found several other holes in the state estimates. Together, they added up to hundreds of millions of dollars. The study pegged the eventual cost at somewhere between $417 million and $1.2 billion, depending on usage patterns.

But neither the state nor the university study considered another crucial variable: disability benefit levels are climbing fast, and will soon reach a maximum of $840 a week. Those higher payments might well serve as an incentive luring more workers to use the family leave plan. And that would drive costs even higher.

It seems almost certain that the employee tax approved as part of this plan will need to be increased, or another source of revenue found, shortly after the family leave program begins. I asked Steve Maviglio, a spokesman for the governor, if Davis would support such a tax increase.

"I don't know," Maviglio said. "I don't know if he's analyzed it."

What? The governor doesn't know about family leave?