WASHINGTON — The Obama administration warned states Thursday it may withhold millions of dollars if they use stimulus money to plug budget holes instead of boosting aid for schools.

Education Secretary Arne Duncan made the threat in a letter to Pennsylvania Gov. Ed Rendell, but his words could have implications for Texas, Arizona and other states.

And they raise the stakes for the White House, which will come under intense pressure from Congress if Duncan does hold back some money.

In the letter, Duncan wrote he is displeased at a plan by Pennsylvania's Republican-led Senate to reduce the share of the state budget for education while leaving its rainy-day surplus untouched. To do so "is a disservice to our children," Duncan wrote.

"Each state has an obligation to play its part in spurring today's economy and protecting our children's education," he wrote.

Duncan said the plan may hurt Pennsylvania's chance to compete for a $5 billion competitive grant fund created by the stimulus law to reward states and school districts that adopt innovations Obama supports.

Rendell, a fellow Democrat, asked Duncan to weigh in.

The education secretary applied similar pressure to Tennessee lawmakers last month after Democrats there blocked a bill to let more kids into charter schools, even though President Barack Obama supports charter schools.

Duncan warned the state could lose out on extra stimulus dollars, and it appears to have worked: This week, lawmakers revived the bill and put it on a fast track toward passage.

In Pennsylvania, the issue is over school spending, which takes up a huge share of state budgets.

State Senate Republicans argue the economy is forcing states across the country to make up for budget cuts with federal stimulus dollars.

Senate Majority Leader Dominic Pileggi said lawmakers can only spend what they have, and they wanted to hold onto the rainy-day surplus in case it's needed once the stimulus money, two years' worth of spending, has run out.

Pileggi said Thursday he is willing to reconsider because the financial picture has worsened since Republicans put their budget together.

"It's certainly something that needs to be re-examined, whether some part of the rainy day fund needs to be utilized in the coming year," Pileggi said.

Rendell is pushing to use the surplus now.

"The state must make sure we do not simply use stimulus funds to cut state funding for schools," Rendell spokesman Chuck Ardo said.

States use rainy-day funds to set aside extra revenue when times are good to use in economic downturns. The surplus funds make it easier for states to borrow money and, when times are tough, help lawmakers avoid tax increases or spending cuts that might worsen a downturn.

In Texas, Arizona and many other states, state lawmakers are still arguing over school spending cuts and the use of stimulus dollars.

Obama did not intend for state lawmakers to simply cut state education spending and replace it with stimulus dollars.

Congress made that tough to enforce; the stimulus law generally does not prohibit states from using some of the money to replace precious state aid for schools. The result is that school districts could wind up with no additional state aid even as local tax revenues plummet.

But Duncan does have leverage; he alone has control over the $5 billion incentive fund. And in some cases, he may be able to withhold some stimulus dollars that have been allocated for a particular state.