Two prominent governors from northeastern states clashed yesterday over President Reagan's proposal to end the deductibility of state and local taxes, as House Ways and Means Committee members searched for a compromise that would prevent the controversial deductibility issue from derailing the overall plan.

Gov. Mario M. Cuomo (D) of New York, the most outspoken critic of repealing the deduction, squared off against Gov. Richard L. Thornburgh (R) of Pennsylvania, who defended the repeal as a vital part of the tax plan during a day-long hearing punctuated by bitter partisan exchanges.

Two other governors suggested ways to limit the deduction, rather than repeal it. Committee members also are looking for a compromise that would partially offset the cost of lowering overall tax rates without unduly affecting states and cities.

Repealing the deduction would raise $34 billion in revenue, the single largest chunk of money in the Reagan plan and an amount badly needed to pay for the proposed lower tax rates.

One compromise under discussion would continue the deduction for state and local income taxes, as well as sales and property taxes, but would limit the amount each taxpayer could deduct. The most popular proposal along those lines would let taxpayers write off the amount of their taxes that exceeded 1 percent of their adjusted gross income.

Another approach is to turn the deduction into a credit, so that taxpayers could subtract a portion of state and local taxes directly from their federal taxes.

A third possibility would be to retain deductibility only for certain taxes, such as property taxes, committee members said.

"I think we're going to come up with a compromise," said Rep. Robert T. Matsui (D-Calif.) "Everyone on the committee realizes this issue has to be negotiated."

Of the four governors who testified before the Ways and Means Committee, only Cuomo was adamantly against any limitation on deductibility. "I'm very much a believer in compromise, but the very genesis of this whole situation is inequitable," Cuomo said.

Thornburgh said the deduction has principally aided "a small percentage of persons with high incomes living in states with high and steeply graduated tax rates."

"I believe that ending this deduction is a reasonable and equitable price to pay for significantly reducing the average American's tax burden," Thornburgh said.

Cuomo said that "depicting this as a deduction for rich New Yorkers is a cynical distortion of the facts."

Under the Reagan plan, which would reduce the top income tax rate to 35 percent, a majority of taxpayers would get a tax cut, according to the Treasury Department.

However, ending the state- and-local deduction would increase taxes for a minority, many of them in states with high taxes, such as New York and the District of Columbia.

Administration officials believe they can persuade Congress to end all state and local tax deductions without compromising.

Govs. John Carlin (D) of Kansas and Richard D. Lamm (D) of Colorado, both testifying on behalf of the National Governors' Association, opposed wiping out the entire deduction but suggested avenues for negotiation.

The two governors said that limiting the amount of the deduction was a "constructive approach."