The abysmal state of Ohio’s revenue forecast has a pair of competing factions offering Gov. Ted Strickland new arguments for two old money-making ideas.

One group is providing Strickland political cover to support tax hikes, by emphasizing the good the money could do for the poor.

The other group has figured a way around Strickland’s campaign promise not to expand gambling, advancing a legal argument that casino-like slots can be added to Ohio Lottery offerings without violating a statewide casino-gambling ban.

Either proposal could gain sudden traction in the next two weeks as lawmakers in the Ohio House struggle to balance Strickland’s proposed $54 billion operating budget that will pay for state programs for the two years beginning July 1. Or, discussion on both topics could wait for the budget debate in the Republican-led Ohio Senate.

Some budget watchers anticipate a giant hole will crop up as the House revamps Strickland’s sweeping package of public-school reforms, based on acknowledgments by the administration that federal stimulus money for the plan is not accounted for properly in its version of the budget.

Others anticipate lawmakers will be tempted to prop up some of their priority programs — many of which are cut or flat-funded in Strickland’s budget plan — and money from either tax hikes or legalized slots will become an enticement.

The Campaign to Protect Ohio’s Future, a coalition of health, human services and education groups, eased into the conversation about higher taxes with the release of a voter survey March 25.

The poll asked respondents, absent specific details, if they would favor a budget proposal that ‘‘increases taxes to avoid cuts in state services.’’ Again without specifics, the questionnaire mentioned rolling back some of the across-the-board income-tax cuts begun under former Gov. Bob Taft, increasing income taxes for those making more than $200,000 a year, and raising some business taxes.

Some 57 percent of Ohioans said they would favor some tax increases to avoid some government cuts. Forty-one percent of respondents opposed the idea and the remaining 2 percent weren’t sure.

Jon Honeck, a fellow with the Cleveland-based Center for Community Solutions, said rolling back the state income-tax rate for the wealthiest 2 percent of Ohioans to 2004 levels would raise about $94 million a year in state revenue. Rolling back the tax cuts for just one year across all income brackets would raise $440 million for the state’s general fund.

Meanwhile, every increase of 0.01 percent in the state’s commercial activities tax on business activity raises an additional $50 million a year, Honeck said.

The campaign’s survey, conducted by the Washington, D.C.-based Garin-Hart-Young Research Group, showed that strong majorities of Ohioans oppose specific cuts contained in Strickland’s budget, including those affecting services for abused and neglected children, at-risk infants, the mentally ill and the hungry.

As attractive as tax increases may be to social welfare advocates, they will be a tough sell to the governor — who has consistently opposed them as making bad economic sense.

That stance increases the likelihood that lawmakers could turn to the $1 billion in quick money that slots at Ohio’s seven horse tracks could raise for the state.

The latest proposal came from the Ohio Racing Commission, which is watching horse tracks around the state crumble and looking for solutions.

Former state tax commissioner Tom Zaino, who sits on the commission, reviewed Ohio’s constitutional language banning casino gambling and doesn’t believe it applies to slots-style video lottery terminals run by the Ohio Lottery.

While Strickland has spoken out against casino gambling almost as often as he’s bad-mouthed higher taxes, the Racing Commission proposal provides him a new political option.

Strickland has already expanded state lottery offerings once, with last year’s introduction of Keno. He said at the time that he does not view adding lottery games as backtracking on his campaign promise to oppose expanded gambling in the state.

The Democratic governor’s argument is that Ohio voters supported creating a lottery to raise money for schools and that, over the years, it has been common practice to change the mix of lottery games available.

Julie Carr Smyth is a correspondent for the Ohio Associated Press.