Divided on both regional and partisan lines, the nation's governors yesterday shelved a proposal for a state takeover of most highway aid and quarreled about the political responsibility for federal budget deficits.

The veneer of bipartisanship that held up through the first two days of the winter meeting of the National Governors' Association cracked on several fronts at the final session.

On a policy dispute that crossed party lines, the governors voted 17 to 15 against a proposal to cancel the 9-cent-a-gallon federal gasoline tax and the present federal highway trust fund and allow states to impose taxes to build and maintain highways.

The proposal, advanced by Indiana Gov. Robert D. Orr (R) with the support of the transportation committee he heads, was shot down by a combination of rural and western governors, who were worried that they would lose on the deal, and some big-state governors who expressed fears that mass transit programs would be shortchanged.

The vote represented at least a short-term setback to the governors' hopes of arranging a swap and "sorting-out" of federal and state responsibilities, but Tennessee Gov. Lamar Alexander (R), association chairman, said the effort might be revived at the summer meeting. "You haven't heard the last of it," he said.

Alexander has tried to steer the governors away from potentially divisive fights over federal budget and tax policies and toward an increased emphasis on state innovations in education, economic development and other fields.

But some of his fellow Republicans were drawn into battle yesterday by a two-fisted Democratic assault on Reagan administration policies.

It began at a breakfast caucus of Democratic governors, who occupy 34 of the 50 governorships. They issued a statement complaining that the administration "has sent to Congress a budget which fails to make the critical investment in our nation's future" and which continues what they called "the unprecedented escalation in Pentagon spending."

Chairman Dan Rostenkowski (D-Ill.) of the House Ways and Means Committee, a speaker at the final plenary session, poured coals on the fire by accusing Reagan of insensitivity to human needs and of a refusal to negotiate seriously with Congress on the budget and revenue needs. "Balancing the budget can't be done with one-liners and slogans," Rostenkowski said.

While Rostenkowski was speaking, New Hampshire Gov. John H. Sununu, chairman of the Republican Governors' Association, signaled to Alexander that he wanted to reply. Accusing Rostenkowski and Congress of succumbing to "the Beltway mentality," Sununu said, "I am tired of you folks telling us we don't understand the realities of the pressures you face . . . . You have become the captives of yourselves."

Because the governors as a group are counting on Rostenkowski's promise to preserve deductibility of state and local taxes in the final version of any tax revision bill, Arkansas Gov. Bill Clinton (D), association vice chairman, tried to smooth things over by asking Rostenkowski how the governors could help bring about a budget compromise.

But Clinton later joined a host of other governors, Republicans and Democrats, in expressing dismay at Rostenkowski's suggestion that he was holding up agreement on a later effective date for a tax bill to pressure senators to act on the House-passed measure.

A number of governors complained that uncertainty over the fate of the Jan. 1, 1986, effective date set in the House bill was freezing the use of tax-exempt revenue bonds in their states. There was applause when Senate Majority Leader Robert J. Dole (R-Kan.) said he favored an early agreement to make the effective date next January.