SPRINGFIELD — Best-case scenario: Gov. Rod Blagojevich’s $10 billion proposal to privatize the state lottery rejuvenates Illinois schools with new textbooks, technology and tutoring.

The changes are such a hit that when the extra money runs out in four years, Illinois officials rush to overhaul education funding so the programs can continue. Meanwhile, the privatization deal produces years of steady, though not spectacular, cash.

But the plan could go another direction.

The worst-case scenario is that the deal doesn’t produce anything close to $10 billion. What extra money is available runs out after four good years, and schools must cancel their new programs or raise property taxes. Then the long-term payments from privatization fail to meet expectations, producing less money than Illinois would have received just by running the lottery itself.

Blagojevich offered a proposal Tuesday to lease the state lottery to a private company or sell stock in it. Schools could get $4 billion over four years from the deal. The remaining $6 billion and any investment income would be parceled out through 2025 to replace the annual lottery revenue Illinois would be giving up.

After that, the state wouldn’t get any money from the privatization deal or the lottery.

The Democratic governor hopes to have the Legislature vote on the proposal in the fall veto session. His aides dismiss the skeptics.

“Embracing the pessimism of the pundits is a recipe for not doing anything or helping anyone,” said Becky Carroll, spokeswoman for his budget office.

Lawmakers and lottery experts, however, say their questions are serious.

Blagojevich hasn’t explained how he concludes the lottery sale would produce $10 billion, but aides insist they are confident in the estimate. The administration says it has been contacted by several potential buyers, and an analyst for Moody’s Investors Service predicts an interest among potential buyers.

But others are more skeptical. They doubt the lottery would bring that kind of money, particularly without some guarantees from the state. Buyers might insist on a guarantee that the lottery’s profits won’t decline or that the state won’t hurt the market by expanding other forms of gambling.

“No one is going to be willing to pay $10 billion upfront unless they could control all of the gaming,” said Kip Peterson, a lottery and gaming consultant for Transnational Market Development Inc. in Georgia.

Then there’s the issue of what happens after the plan’s first four years.

During those four years, Blagojevich intends to spend $4 billion from the lottery deal, along with enough other state money to bring the total to $6 billion. That would pay for aid to at-risk students, new technology, up-to-date textbooks and $1.5 billion in new school buildings.

But after four years, all that extra money would vanish.

Blagojevich’s aides predict the state will step in with some new source of money. With schools depending so heavily on the money, officials will have no choice but to come up with more, the argument goes.

Yet there’s also a chance that officials wouldn’t act. Local authorities would have no options but to raise property taxes or dramatically cut back services, said tax expert Ralph Martire.

“After four years, what do we do when we hit that cliff — jump off? There is nothing to take the place after the big infusion from the lottery,” said Martire, executive director of the Chicago-based Center for Tax and Budget Accountability.

After those four years, the privatization plan is supposed to generate about $650 million a year for the state, a little more than Illinois schools now typically get from the lottery.

The administration argues that having that income guaranteed through 2025 and then losing it entirely is a better deal for the state than depending on the ups and downs of annual lottery revenues.

Experts wouldn’t comment on whether the state can count on getting that $650 million a year from the privatization plan, saying they just don’t have enough details about the proposal.

But even skeptics see some potential benefits to the governor’s plan.

Martire said it could pressure lawmakers to change how the state pays for education and other essential programs. And Peterson said revamping lottery operations might be helpful.