Five months after Democratic Gov. Richard F. Celeste took the helm of this depressed industrial state, the Republicans gleefully released a poll showing that his once-formidable popularity has plunged to a record low.

It is not difficult to figure out why. Faced with a billion-dollar budget deficit, Celeste pushed a 90 percent income tax surcharge through the state legislature in three weeks, and he is still feeling the backlash. Fellow Democrats recently shot down his latest initiative, a proposed tax on business services.

A Rhodes scholar and former Peace Corps director, Celeste shows signs of being an innovative leader, but a series of political missteps, from increasing his staff to accepting consulting fees from his campaign committee, has kept him off balance.

"Dick Celeste is like a farmer walking through his pasture past a lot of cow piles, and he hasn't missed one yet," said Paul Gillmor, the Republican Senate leader.

Celeste's near-landslide victory last fall led a Democratic sweep of most of the midwestern gubernatorial races as several veteran Republicans--James A. Rhodes in Ohio, William Milliken in Michigan and Albert Quie in Minnesota--did not run for reelection. Now, however, their Democratic successors are finding it painful to take the steps needed to balance their sagging budgets.

Michigan Gov. James J. Blanchard, who has raised the state income tax by 38 percent and cut $225 million in state spending, is facing a small but growing recall movement led by conservative groups.

"There is a backlash, and we're experiencing it right now," a spokesman for Blanchard said. "We could have laid off every worker in the state and the budget still wouldn't have been balanced, but a lot of people are very upset."

Wisconsin Gov. Anthony Earl has cut spending 10 percent, adopted a 5-cent cigarette tax increase and canceled $500 million in scheduled property tax credits. Now he is proposing another $500 million in budget cuts, much in aid to local governments.

And in Minnesota, which raised taxes several times last year, Gov. Rudy Perpich has proposed retaining a 10 percent income tax surcharge and a higher sales tax, may cut spending further and also plans to cut back on property tax relief.

But the statehouse blues seem most pronounced here in Ohio's capital, where Celeste's top aides begin by trying to convince voters that his doubling of a temporary income tax surcharge, amounting to a 27 percent real increase, did not violate a campaign pledge.

"People are angry at Dick Celeste for raising taxes," said Ohio budget director Cristina Sale. "I get on a radio talk show and nine of 10 questions are on taxes. Some people think he promised not to raise taxes. He didn't, he just simply avoided the issue."

Republicans in the statehouse have refused to provide a single vote for Celeste's tax hikes, preferring instead to rail against the governor's proposed spending increases for education, welfare and economic development. They also have refused to offer any budget alternatives or to say how they would cut spending.

"There are no Republicans to be held accountable in Columbus today," said Celeste. "It's too easy to just be against taxes. My only hope is that people will see it for what it is."

Still, Celeste does not dispute the accuracy of a GOP poll showing that 73 percent of the voters oppose his income tax surcharge and only 23 percent approve of his performance as governor.

"I understand people being angry about it, because I don't like taxes either," he said. "But we didn't have a whole lot of room to move. We had to get the state on a solid financial foundation. If I could have achieved that simply by cutting, I would have."

However, a local press club gave Celeste its "Boner of the Year" award after these incidents:

* Reporters found that Celeste's campaign committee paid him $45,000 in consulting fees last year. "I'm a candidate with a wife and six kids and that's how we ate," Celeste said. "Being able to eat got me elected." But state GOP Chairman Michael F. Colley said that "people were incensed. They made political contributions and didn't expect him to spend it for his personal support."

* Celeste asked private business groups to help pay a $102,000 salary to his new director of economic development, who was hired away from the local Chamber of Commerce. After an uproar, the director eventually agreed to accept a $63,000 state salary.

* Celeste won praise for including five women and three blacks in a broad-based cabinet that includes a former nun and a three-star general. But after campaigning on a "Buy Ohio" theme, he drew flak by bringing in six top officials from out of state.

* Celeste fired hundreds of "unclassified" state employes, saying they were Republican patronage appointees, but was criticized for including many low-level secretaries and clerks.

* And after cutting the state budget by $280 million, Celeste expanded his personal staff from 19 to 31, including two full-time assistants for his outspoken wife, Dagmar.

While fighting the "big spender" label, he has received counterpressure from liberal interest groups such as the teachers' unions, which complain that his proposed 21 percent boost in public school funding is inadequate.

Celeste also argued that lawyers, accountants, architects and other professionals are not paying their fair share of taxes, but business lobbyists descended on the capital this month to defeat his 4 percent excise tax on professional services.

"Dick hasn't lost the ball game, but he certainly lost this inning," said tax commissioner Joanne Limbach, whose planned tax relief for middle-income families was killed in the process.

In the meantime, Celeste is banking on a 27-page "action agenda" that includes state grants to business-university partnerships, doubling the tourism budget, repairing highways and bridges, providing more aid for vocational schools and job training and creating a housing finance agency, which last week offered $300 million in low-interest mortgages that had thousands of people here waiting in line for days.

Aides also are studying ways to apply high technology to older industries, such as finding cleaner ways to burn Ohio's abundant supply of high-sulfur coal.

"I'm frustrated with programs that take six years to design," Celeste said. "We have an economy in transition in a heavy manufacturing state like Ohio. The recovery here is going to be slow, and not as many people will be working in the long run. Traditional political rhetoric will not do to deal with these kinds of changes."