PHOENIX — Some good news for individuals in the new federal stimulus package could end up losing Arizona tens of millions of dollars in state tax revenues, at least in the short term.

Richard Stavneak, staff director of the Joint Legislative Budget Committee, pointed out to lawmakers on Tuesday that one key provision in the American Recovery and Reinvestment Act provides a $400 a year federal tax reduction for individuals — $800 for couples — this year and next.

That tax break will come not in a check to taxpayers but instead be spread out over the remaining paychecks, with the federal government deducting a little less each time.

The problem, Stavneak explained, is that the amount deducted in state income taxes from each worker’s paycheck is a percentage of the federal withholding. That means the federal change automatically means lower state withholding — and less cash going into the state treasury.

Technically speaking, nothing in the federal law changes anyone’s state income tax liability. And Arizona residents will owe as much to the state next month — and the April after that — as they would without the change in federal law.

In the interim, though, Stavneak estimated Arizona will collect $73 million less from worker paychecks between now and the end of the state budget year on June 30. And he figures the cash loss for next budget year at $37 million.

It will only be the budget year after that when things catch up, with the state collecting an extra $109 million as Arizona residents, having had less money than anticipated withheld from their checks, pay up.

Rep. John Kavanagh, R-Fountain Hills, who chairs the House Appropriations Committee, said he wants to keep the cash coming in at the current rate, whether by changing state law or alternations made in the withholding schedule by the Department of Revenue. Kavanagh said it protects the state treasury. And it ends up costing Arizonans no more in the end, other than the loss of the use of the cash in the interim.

More problematic for the state are some other provisions in the stimulus law.

One lets taxpayers exclude up to $2,400 of unemployment compensation from their federally adjusted gross income. Another provides a deduction for the sales taxes paid on the purchase of new vehicles valued at $49,000 or less.

The problem here is that Arizona is a “piggy back’’ state. Residents compute their state income taxes each year starting with that federally adjusted gross income. A lower figure on that line on the federal form automatically results in lower state tax liability.

Stavneak said the state Department of Revenue estimates the loss for next budget year from those two changes at $22.5 million.

There is a solution: Amend the state tax law — and the tax forms — to require Arizonans to add back in the deductions taken on the federal form. But Sen. Russell Pearce, R-Mesa, Kavanagh’s counterpart in the Senate, said he is loath to create more work for Arizona taxpayers.

One other change in the stimulus package also could affect the amount of money Arizona lawmakers have to spend.

Generally speaking, if a debt is forgiven, the amount is considered taxable income. The federal law allows companies that have debts cancelled to defer payment of the taxes due, spreading them out over five years.

The reduced federal income for businesses is reflected, as with individuals, in lower state taxable income. The Department of Revenues forecasts the loss for next year at $53 million, declining to $28 million the budget year after that.