PROVIDENCE — Giving state prison inmates a raft of new early release opportunities was supposed to make a big dent in the prison population and save the state millions of dollars in a tough budget year.

Inmates –– with the exception of sex offenders and those serving life sentences — could earn extra days off their sentences for good behavior and participation in rehabilitation and treatment programs. But the number of prison inmates is up, not down.

The budget approved by lawmakers — and signed into law by Governor Carcieri last June — assumed the early-release initiatives would reduce the prison rolls by 211 inmates. But only 50 inmates have qualified so far, while the “awaiting-trial population” has ballooned from an average of 694 at any given time last year to 790 during the first several months of this year.

Compounding the dilemma: a virtual hiring freeze, after a flood of retirements, has forced the Department of Corrections to rely heavily on unbudgeted overtime — at what would be an annualized cost of $9.7 million — at the Adult Correctional Institutions.

And other state agencies are having even bigger — and more costly — problems living within their budgets, according to a quarterly spending report issued yesterday that sheds further light on how the state ran head-on into a potential $357.4-million deficit only three months into the current budget year.

It’s a combination of deflated revenues, overly optimistic budget cuts and overspending both this year and last when the state dipped into its rainy-day fund to cover an unprecedented $38.4-million deficit that it is required, by law, to replenish this year.

Last week, the top budget advisers to the governor and legislature pinpointed the size of the state’s likely revenue shortfall: $233.6 million.

The national financial meltdown has taken a huge bite out of tax receipts. Lottery collections are trailing expectations. The revenue shortfall accounts for two-thirds of the state’s emerging mid-year budget problem.

The report released yesterday details $127.6 million in unbudgeted spending, including the tens of millions of dollars in “unachieved savings” that may have looked good on paper but have yet to pan out; the retroactive arbitration-settlement of a long-running dispute with the Rhode Island Brotherhood of Correctional Officers, and a proposed $10-million settlement of the state’s potential liability in the devastating Station nightclub fire that claimed 100 lives.

Along the way, Republican Carcieri urged the overwhelmingly Democratic legislature to bank, for example, on a total of $66.6 million in budget savings from “Medicaid reforms” that are predicated on many fewer people going into hospitals, nursing homes and group homes, and the federal government giving state officials more flexibility on how and where they spend Rhode Island’s share of the Medicaid pie.

The savings were predicated on an Oct. 1 federal approval.

The state is still waiting, though Gary Alexander, director of the Department of Human Services, suggested last night that the state is moving ahead with what he called its “NH diversion and transition” initiative, which appeared to be his shorthand for a reduction in the number of people in nursing homes under the state and federally subsidized Medicaid program.

In an e-mail, he said: “The state is moving forward with this initiative with or without the waiver. The waiver will allow for greater flexibility for levels of care which will thus provide for more appropriate placements of individuals. We are thus accruing savings but not at the rate contemplated with the full-blown waiver.”

Though asked repeatedly yesterday to clarify what he meant, he would not.

Other overruns were attributed to the delayed launch of three other major cost-saving initiatives, including: the mandatory use of generic drugs by participants in RIte Care, the state-subsidized health insurance program for families with children, the use of a preferred drug list and the extension of “premium co-sharing” to families farther down the income ladder.

A $9.8-million savings had been hinged on the first item alone, which has since become snagged, according to Alexander, on a federal requirement that a “medical necessity review” be conducted. “We are trying to move forward with this initiative even though we have challenges,” he said without elaboration.

Alexander attributed the delayed start of the premium cost-sharing on the need for “computer program modifications and prior legal notice.” He said the requirements kicked in on Nov. 1, with families at the lower end paying anywhere from $45 to $106 monthly, depending on income, and those at the slightly higher end paying $114.

All together, yesterday’s report reflects $49.4 million in potential overspending this year by the Department of Human Services and the Department of Mental Health, Retardation and Hospitals under the Medicaid banner.

And even that doesn’t tell the whole story because the report also reflects a potential $18.7 million in unbudgeted spending by the Department of Children, Youth and Families as a result of a “Medicaid Billing Methodology Change.”

Translated: the state’s child welfare agency felt compelled, in light of newly “refined” federal regulations, to take a look at how it was divvying up, between the state and the federally subsidized Medicaid program, the costs for treatment, assessment and just plain room and board for youngsters under its jurisdiction in group homes and other residential settings.

According to DCYF’s chief financial officer, Brian Peterson, this “time-study” determined Rhode Island wasn’t entitled to as much money as it had hoped. He said the agency also underestimated — at a further cost of $3.4 million — the number of youngsters “18 and older” that it would have on its rolls. He said the budget assumed 198 youngsters, when the actual count has been closer to 258 at a cost of more than $50,000 each.

Lest anyone think the potential deficit is Carcieri’s fault for over-estimating potential budget savings, spokeswoman Amy Kempe argues otherwise. At the start of the budget debate last winter, she notes, Carcieri proposed a series of unpaid days off for state workers. They didn’t materialize, but the lawmakers booked the savings anyway, as they did the potential savings from eliminating 243 jobs they restored in housekeeping, food and counseling services that he unsuccessfully sought permission to “privatize.”

For good measure, the state budget office also used the quarterly report as a vehicle to draw attention to a $1.7 million end-of-year surplus the part-time General Assembly rolled over from last year to this year, giving the part-time lawmakers a total of $35.8 million to spend this year.

kgregg@projo.com