The executive committee of the National Governors Association yesterday voted 7 to 1 to clear a bipartisan plan aimed at slashing future budget deficits by two-thirds, but the proposal ran into a cross fire that may jeopardize its passage when all of the governors vote Tuesday.

"I have to fiddle with it enough to get some Democratic votes," said association Chairman Scott M. Matheson, the Democratic governor of Utah and prime mover in the effort to get the governors into the national debate on budget policy. Passage Tuesday will require a two-thirds vote.

Even though the draft resolution calls for major cutbacks in President Reagan's defense program and hints at the need for higher taxes, Republicans denied it is a slap at the president and, for the most part, praised it.

Richard S. Williamson, assistant to the president for intergovernmental affairs, said, "We could have killed it" by expressing presidential opposition, since Republicans have five of the nine executive committee votes. "But if it's going down, we'd rather the other side do it."

Several of the newly elected Democratic governors seemed inclined to do just that. Newcomers Toney Anaya of New Mexico and Anthony S. Earl of Wisconsin joined veteran Bruce Babbitt of Arizona in condemning what Babbitt called the "manifestly inequitable" policy of expanding the defense share of the budget while cutting back on social programs.

On the other flank, Pennsylvania Gov. Richard L. Thornburgh (R) questioned the governors' expertise in the defense area. "Our reach may be exceeding our grasp, and our credibility may begin to erode," he said.

But Thornburgh joined in clearing the resolution from the committee, leaving the sole negative vote to Maine Gov. Joseph E. Brennan (D). North Carolina Gov. James B. Hunt (D) did not vote.

The resolution, which Matheson said had undergone at least five revisions, is aimed at slashing the projected fiscal 1988 deficit from $267 billion to $90 billion. Matheson and his chief partner and designated successor as chairman, Illinois Gov. James R. Thompson (R), said this is necessary to sustain the economic recovery and reduce fiscal pressure on the states.

It calls for saving $294 billion from defense cutbacks or revenue increases in the next five years, $169 billion in domestic savings and $69 billion in reduced interest costs.

"There's plenty of running room in this resolution," Thompson said, arguing that "it is not an attack or criticism of any administration, party, house or committee of Congress." But Babbitt called it "a lowest common denominator resolution," which does not declare "progressive principles of shared sacrifice."

With Democrats holding a 34-to-16 majority among the governors, some of them are fearful that approval of the resolution in its present form would undercut efforts to sharpen the budget and tax issue in Congress and on the campaign trail.

But Matheson said his efforts had been encouraged by House Budget Committee Chairman James R. Jones (D-Okla.) and Senate Budget Committee Chairman Pete V. Domenici (R-N.M.).

The resolution recommends no specific revenue-raising measure. It endorses a presidential commission's plan for financing Social Security and calls for a slowdown in other disability and retirement programs.

"Means-tested" programs such as food stamps and Medicaid should receive "almost full funding," it says, while domestic discretionary programs--including most federal grants to states--should be pegged to grow at three-fourths the rate of inflation.

The last provision, Matheson conceded, is actually a sweetener for the states, because governors accepted a freeze on federal grants last year and initially were ready to accept another freeze for next year. He said that the governors felt that their first-year Reagan cuts were "pretty harsh" and that they should not be asked to sacrifice again.

The resolution, with its specific defense targets of 4 to 6 percent real growth in 1984-85 and 3 to 5 percent in the 1984-88 period, represented the advice of Raymond C. Scheppach, who moved over from deputy director of the Congressional Budget Office to become executive director of the governors' association a few months ago.

Thornburgh questioned whether governors know if these numbers "have any relationship to preserving the national defense," but Vermont Gov. Richard A. Snelling (R) replied that "you don't have to be an MX missile expert to say there's a level of defense spending that really harms the country."

Aside from the budget debate, the governors spent much of their opening day on law-enforcement questions.

Attorney General William French Smith and FBI Director William H. Webster asked for their help on the drive to curb drugs, and Chief Justice Warren E. Burger solicited their support for federal and state funds for improving state courts and training their judges.

Last night, the governors were guests at a White House dinner, and they are scheduled to meet with the president today.