In Ohio, the governor, who has made a career of beating "high-tax Democrats," has been forced to seek higher taxes himself--and is facing a rebellion of some of his own conservative Republicans.

In Washington, the state has already been forced to borrow from the banks to pay its bills and the fiscal and political noose is drawing even tighter.

In South Carolina, the governor ordered a 7 percent across-the-board cut in all state agencies earlier this year. Now, he is preparing to absorb another $124 million in federal cutbacks, some of which will hit the typical welfare family of three living on an $87-a-month stipend that is the second lowest in the nation.

In New Jersey, Ronald Reagan's budget cuts have become a major barrier to the Republicans' chances of capturing the governorship in next month's election.

And in California, where Reagan first practiced his campaign against "waste, fraud and abuse," the new cuts find his Democratic successor trying to convince voters that the cupboard really has turned bare.

Those are some of the political problems described by Washington Post special correspondents in a survey of the immediate consequences of the federal spending cutbacks that go into effect today.

About one-third of the legislatures are meeting in special or extended sessions this autumn to deal with the changes in the fiscal picture that have arisen since they closed shop earlier this year.

That picture is far from uniformly bleak or contentious. In Louisiana, for example, the special session is needed mainly to carve up a $140 million to $170 million severance tax bonanza from the state's energy wealth. "People are being very creative about the uses of that money," one observer said.

In most of the states, there will be no pitched political battles fought this fall, either because they are being postponed to the regular legislative session in January or because there is a conservative consensus that nothing will be done now to offset the program cutbacks that are the consequences of scarcer federal dollars.

In most of the states, the picture is one of surface harmony, because most politicians--Republicans and Democrats, governors and legislators--are extremely reluctant to suggest increasing state taxes further when Washington is cutting federal taxes. The Tax Foundation says 30 states have already taken action to raise revenues by $2.5 billion a year.

This reluctance to increase taxes further leaves a lot of unhappy mayors and state-local program administrators holding the bag or preparing their own "RIF notices" for their employes. But for now, at least, those folks are politically so much in the minority that they are unable to muster many allies in the state capitols.

Across the Deep South, where the cutbacks mean reductions in what were already some of the nation's most meager income support and social services programs, Democratic governors and legislatures are swallowing the entire Reagan program.

South Carolina Gov. Richard Riley (D), who faces reelection next year, ordered his 7 percent across-the-board reduction in state spending earlier this year to avoid syphoning more then $3 million from the state's emergency reserve funds. Now he must make more cuts because of the Reagan administration cutbacks and is trying to prune administrative costs in an already slimmed-down state bureaucracy, meanwhile organizing a "volunteerism council" to mobilize unpaid helpers in health and social-service agencies.

It is against that background in dozens of states that the political trials of Ohio Gov. James A. Rhodes (R) seems so striking. Rhodes has been governor for 16 of the last 20 years, most often winning against Democrats who had raised taxes or, he said, might do so if elected.

Now, he is seeking what he calls a "temporary" $1.75 billion tax increase and is being opposed by a caucus of conservative Republicans who hold the votes he needs to pass his program. Last week, a combination of that Republican oposition and a Democratic drive for a permanent tax package overwhelmed Rhodes. Today, the state House of Representatives is expected to vote on the Democratic alternative, with the outcome very much in doubt.

While the program is focused primarily on the state's chronic school-finance crisis, the federal budget cuts have put added pressure on a state budget that already has been trimmed 7 percent.

The current tax controversy could cast a shadow on Rhodes' expected 1982 bid to oppose Sen. Howard M. Metzenbaum (D-Ohio), but a much more immediate political test will come in next month's New Jersey gubernatorial election.

By coincidence, Rep. James J. Florio, the Democratic nominee, and former state representative Thomas H. Kean, the Republican contender, will meet tonight in the second debate of their campaign. A Kean strategist said yesterday, "I know he's going to throw the budget cuts at us."

Kean has identified himself with the Reagan economic strategy, endorsing a series of corporate and individual tax cuts for New Jersey that, he says, would complement the Reagan-sponsored federal cuts and spur the state's lagging economy.

But Florio contends that the tax cuts are unrealistic and the spending reductions from Washington damaging, not just to the poor, but to middle-class commuters, college students and others. It is now Florio, much more than Kean, who is trying to cast the election as a referendum on Reaganomics.

The states where the political fallout from the budget cuts is likely to be most severe are those where declining local economies are already putting governors in a squeeze. That is true of many of the Midwest states, where the auto industry is important. Most of those states have Republican governors who face reelection next year.

But the most severe problems at the moment may be in Washington State, whose lumber and wood-products industry has been crippled by the housing slump caused by high interest rates.

Freshman Gov. John Spellman (R), elected last November on a pledge not to raise taxes, has been forced to borrow almost half-a-million dollars from banks to pay bills and has called the legislature into session next month to seek a sales tax increase.

Like Rhodes in Ohio, he is facing a rebellion from his fellow Republicans, who say the state should slash spending further and make no effort to cushion any of the loss of $370 million to $400 million in federal funds. But education officials have filed suit already to force the state to meet its school funding obligations, and the squeeze is tightening on Spellman.

Spellman may count himself lucky that he is in the early months of a four-year term. In New Hampshire, where taxes are always the dominant issue because of the state's tradition of having neither a sales nor an income tax, Gov. Hugh Gallen (D) is feeling the strain a year in advance of his third-term bid.

He is expected to call a special session of the legislature next year to seek some form of additional business tax to cushion $80 million in federal aid cuts. But state Senate President Robert Monier, already announced for the Republican nomination to oppose Gallen says, "there is no way I will support making up whatever those losses are from state funds."

Although Democrats have the majority of the governorships, a disproportionate share of the political pain of the cuts is likely to focus on Reagan's fellow Republicans, one way or another. In Rhode Island, for example, Gov. J. Joseph Garrahy (D) and the leaders of the Democratic-controlled legislature have decided there is no point in having a special session, because there is no room in the state budget to make up for the $21.5 million in federal-aid cuts.

Instead, says The Post's correspondent, "Rhode Island Democrats are enthusiastic about using the cuts as weapons against the 1982 reelection bids" of two Republican officeholders, Sen. John H. Chafee and freshman Rep. Claudine Schneider.

One Democrat who cannot comfortably play that game is Reagan's successor, Calif. Gov. Edmund G. (Jerry) Brown Jr. The California legislature recessed in September without passing a bill that would have squared state law with the new federal welfare cuts. As a result, the state faces a $75 million overrun in the next nine months. The state constitution forbids a deficit budget.

Gone is the healthy surplus that made it possible for Sacramento to cushion communities against the earlier effects of the Proposition 13 property tax rollback ordered by voters in 1978. And Brown is headed into his 1982 Senate campaign with the kind of problems that state politicians may well find all the more common in coming months and years.