The chairman of the Senate Budget Committee told the nation's governors yesterday they cannot expect to be spared from major domestic cutbacks either by slashes in defense spending or a federal tax increase.

In a discussion with the executive committee of the National Governors' Association, Sen. Pete V. Domenici (R-N.M.), the budget panel chairman, said that members of Congress have accepted President Reagan's judgment that the problems of agriculture, mining, timber and heavy manufacturing, "can't be solved" simply by restoring some budget cuts.

While conceding that these problems are "traumatic" for many states, Domenici contended that "no one has a blueprint for government expenditures which will substantially relieve these problems."

Describing the new Gramm-Rudman-Hollings budget process as "a planned train wreck," Domenici said there was "far better than a 50-50 chance" its $144 billion deficit target will be reached -- but far less likelihood that cuts to states will be spared.

The governors got better news about the prospects for deductibility of state and local taxes and the handling of tax-exempt bonds in the Senate tax bill from Sen. Bill Bradley (D-N.J.), a member of the Senate Finance Committee.

Bradley said he was "fairly sure" that state property and income taxes would continue to be deductible, but was less certain about sales and personal property taxes. The House version of the bill preserved deductibility for all these taxes, but Reagan has urged the Senate to eliminate deductibility across the board.

Bradley also said he thought that the Senate would lift what he called "a rather arbitrary" House cap on state and local tax-exempt bonds and probably expand the list of permissible uses for those bonds.

Bradley urged the governors to press the chairmen of the House and Senate tax-writing committees for a joint statement this week on the effective date of any tax-revision bill. Bradley said that Sen. Bob Packwood (R-Ore.) and Rep. Dan Rostenkowski (D-Ill.) have indicated separately that the new law, if passed, would take effect either next Oct. 1 or Jan. 1. "But we need to get them on the record," he said, to allay the doubts of businesses and governments about the rules for major capital expenditures.

Secretary of Education William J. Bennett told the governors that the administration's education voucher proposal "is not anti-public school; it's anti-bad school." Bennett said that in some localities where students can pick their schools, "magnet" public schools are pulling students out of private schools.

The governors seemed more preoccupied with the pending budget cuts, which their association estimates would cost them $16 billion in spending authority in fiscal 1987.

When Arkansas Gov. Bill Clinton (D) asked Domenici if Congress could consider "raising some revenues for deficit reduction" in conjunction with tax-revision, Domenici replied: "I could, but, no, I don't believe it will be done." Pointing out that Reagan has informally endorsed a new energy tax to "balance" the tax bill, he said, "Nobody is moving in the direction of using higher taxes for deficit reduction."

Domenici, who has generally supported lower defense spending than Reagan has requested, said those who believe that the Gramm-Rudman-Hollings targets can be reached largely by slashing defense will be disappointed. "I don't believe you can have a substantial change in the middle of a defense buildup," he said.

New Jersey Gov. Thomas H. Kean (R) complained about the "irrationality" of the Gramm-Rudman-Hollings process and questioned the wisdom of cutting back on education and job-training programs that he said "ought to be looked at as investments that will produce long-term growth."

Domenici replied: "I don't know what ever got into you to think we are rational up here."