The National Governors Association yesterday threw its weight behind the bipartisan drive to curb future budget deficits by slowing down both defense and domestic spending and raising taxes.

By a vote of 30 to 10 the governors passed the policy resolution aimed at cutting projected deficits from $267 billion to $90 billion by 1988.

Their chairman, Utah Gov. Scott Matheson (D), said the action meant that for the first time the governors "are wrestling with the full weight of the federal budget," instead of just the financing of programs that directly affect the states.

Their effort was applauded in speeches just before the vote by Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) and House Budget Committee Chairman James R. Jones (D-Okla.).

But it came only after Matheson and his allies among the senior governors in the leadership of the association were able to quash a rebellion led by newly elected Democrats, who wanted the organization to call for cancellation of the 1983 tax cut and further defense spending cuts.

Their substitute, sponsored by Wisconsin Gov. Anthony S. Earl (D), was defeated, 25 to 16, after one of the liveliest debates in the recent history of the organization. Ten of the 16 who supported Earl then voted against passage of the bipartisan compromise.

Republican governors, who now comprise only one-third of the association's membership, unanimously supported the leadership resolution, even though President Reagan had condemned its defense and revenue sections in a meeting with the governors Monday.

Richard S. Williamson, assistant to the president for intergovernmental relations, said that, despite the president's vehement objections to parts of the package, the White House was "pleased" with the resolution, because it put the governors on record as calling for reductions in most entitlement programs.

The organization's Republican vice chairman, Illinois Gov. James R. Thompson, delivered an emotional appeal for the resolution, saying that "if we falter, Congress may falter" from making the necessary budget cuts. "And if Congress falters, the country will collapse back into a recession."

South Carolina Gov. Richard W. Riley (D) had no trouble getting approval of amendments making explicit reference to "jobs for the millions of Americans who need work" and saying that any new taxes should "not unfairly burden already hard-pressed lower- or middle-income Americans."

But that did not satisfy some of the newly elected Democrats and their allies.

Earl offered a substitute calling for cancellation of the scheduled 1983 tax cut and delay of tax-indexing, plus a much harder look at the defense budget.

It said "the primary objective of federal fiscal policy should be to provide jobs for those who have been put out of work by the recession," even if it means higher spending for some domestic programs.

In their breakfast caucus, before the final plenary session, the Democratic governors had unanimously adopted Earl's substitute resolution as a statement of party position.

But some wavered at pushing it into the conference, where it would clearly have scared off Republican support.

Virginia Gov. Charles S. Robb (D) was one.

"I support the Earl position personally," he said in debate, "but will vote against it for the sole purpose of strengthening the bipartisan position of the National Governors Association."

Robb also said he had some personal "reservations about the specificity of defense cuts and the tacit acceptance of out-year deficits" in the leadership resolution he backed.

Maryland Gov. Harry Hughes (D) also voted against the substitute and for the original resolution, even though he said in an interview, "I feel very strongly that defense should be held down, indexing be deferred and the third year tax cut be reduced. But it's very important we get a resolution out of here."

Other Democrats were less flexible. Earl argued that "you can be bipartisan without being bland," and Ohio Gov. Richard F. Celeste (D), another newcomer, urged the governors to tell Congress plainly to forget further tax cuts while his state and most others are raising levies.

Kentucky Gov. John Y. Brown, chairman of the Democratic governors' caucus, complained that the original resolution was "basically stay the course," adding, "I don't know why as governors we want to be part of the Reagan failure." But his view did not prevail.

In its main provisions, the adopted resolution endorses:

The bipartisan Social Security package; holding most discretionary domestic programs, including the major federal grant-in-aid programs, to a growth rate 25 percent below inflation; "almost full funding" of food stamps, Medicaid, Aid to Families with Dependent Children and other means-tested entitlements; restraint on non-means tested entitlements; a slowdown in the defense buildup to between 3 and 5 percent in the 1984-88 period, about half the rate Reagan has urged, and some unspecified amount and kind of revenue increase, as needed.

The resolution projects total five-year savings of $532 billion, with $169 billion on the domestic side, $294 billion of defense cuts and/or revenue increases, and $69 billion in interest savings.