A partisan debate erupted today at the opening of the National Governors Association meeting, with Vice President Bush claiming that the "surging economic recovery" has vindicated the administration's economic policies, and Democratic governors saying they do not believe that is so.

While Bush keynoted the opening session of the 75th annual meeting with an upbeat description of the economic scene, Utah Gov. Scott M. Matheson (D), the association chairman, warned that it could be just "a blip on the horizon."

Matheson said that unless President Reagan relents on his opposition to any kind of tax increase in the next two years and Congress moves to close the large budget deficits, the recovery will stop short.

"If we're not willing to face up to more taxes--and make the decision soon--we can kiss the recovery goodbye," Matheson said.

Bush sounded a strongly partisan note in his speech to the governors, two-thirds of whom are Democrats. He claimed credit for the administration in trimming inflation and interest rates, cutting taxes and slowing the growth of federal spending. Bush said no one would want to go back to the conditions of the final two years of the Carter administration, when, he said, families on fixed incomes lost 20 percent of their real income to inflation.

"The charge is leveled against us of being unfair," Bush said, "but that was surely unfair to families trying to make ends meet."

The Bush-Matheson battle today was a replay of the fight that broke out last winter, when the governors' association, plunging into the budget debate for the first time, passed a resolution calling for cutbacks in both defense and domestic spending and consideration of tax increases, in order to reduce federal deficits.

Reagan strongly rejected the tax and defense portions of the governors' program. But Matheson today claimed that the budget resolution adopted by Congress "bears the unmistakable print" of the governors' recommendation. He said his only concern is that Congress may balk at carrying out its provisions because of Reagan's opposition to any tax increases before 1985.

Bush said, "We know that the current federal deficits represent a challenge, and that when the federal government engages in its present massive borrowing, it squeezes resources away from the private sector."

But he defended the administration's insistence on securing the third year of the tax cut, and said the answer to deficits "cannot possibly be to raise taxes and spend money just as this recovery is gathering strength . . . . We remain strong in our belief that budget cuts are the right way to reduce deficit spending."

Democratic reaction was predictably critical. Wisconsin Gov. Anthony S. Earl (D) said, "To say the way to reduce deficits is to cut taxes is an amazing message to deliver to governors, the majority of whom have had to raise taxes to balance their budgets."

A prominent Republican, Tennessee Gov. Lamar Alexander, said the administration had to take some of the blame because "the national government's deficit this year is more than the states are spending on everything. That means Washington is broke."