TRAVERSE CITY, MICH., JULY 26 -- Vexed that a possible welfare revision breakthrough may be slipping through their fingers, the nation's governors tried today without immediate success to narrow disagreements between the Reagan administration and the Democratic Congress that threaten enactment of legislation this year.

In public sessions and private discussions with sponsors of the House and Senate bills and White House aides, the governors tried to make the case that it would be "tragic and unnecessary," as New Jersey Gov. Thomas H. Kean (R) put it, for the effort to fail "when we're all so close together."

But at the end of the meetings the differences were at least as great and chances of compromise that could avert a presidential veto as fragile as they had been. "Fundamentally, we're not that far apart," said Delaware Gov. Michael N. Castle (R), head of the National Governors' Association task force on welfare reform, "but when it comes to working out the costs and details, it gets difficult."

After their meetings with Rep. Thomas J. Downey (D-N.Y.), who is managing the bill cleared by the House Ways and Means Committee, Sen. Daniel Patrick Moynihan (D-N.Y.), sponsor of the principal Senate legislation, and White House officials including Frank J. Donatelli, assistant to the president for political and intergovernmental affairs, it was hard to find governors optimistic about compromise.

Downey reiterated that the House would pass this year, either as separate legislation or as part of an end-of-session reconciliation bill, its version of welfare revision, which Donatelli told the governors faces an almost certain veto from President Reagan.

Moynihan would offer no forecast on his bill, which he introduced last week with 27 cosponsors and which mirrors the governors' basic preferences. He said, "We ought to be able to do this {pass welfare reform} and if we don't it will be only because the White House put its back against it."

The governors, the White House and the congressional Democrats favor changing the existing Aid to Families with Dependent Children (AFDC) program to put more emphasis on financial responsibility of parents, job training and employment.

But a governors' association official involved in the negotiations said the discussions have snagged on four points: the extension of coverage to families where both parents are at home but unemployed; differences over the age a child must be before a single-parent mother is required to seek work or training; the variety of corollary federal-state aid programs for which governors could seek waivers from the administration, and the cap on additional spending, if any, for transition services to those attempting to work their way off welfare.

Aside from the welfare debate, which took center stage on the first full day of the association meeting here, the governors heard Kean report that they had made "remarkable" progress on education in the first year since they adopted the mutual pledge at last year's meeting in Hilton Head, S.C., of a five-year effort to improve schools.

After hearing six governors and several educators highlight actions in individual states, Kean said the comprehensive national survey the governors released today showed "a revolution going on state by state." The efforts involved not only higher salaries for teachers and a variety of performance-based pay schemes, but experiments in restructuring schools and curriculums, credentialing teachers and forcing colleges to evaluate their students' educational progress.

This afternoon, Chrysler Corp. Chairman Lee Iacocca told the governors that while all of them are "really fighting for jobs" for constituents, "nobody in Washington is fighting for American jobs. Without a coherent policy in Washington," he warned, "you're fighting for pieces of a smaller and smaller pie, and I'm afraid you'll soon be fighting over the crumbs."

Iacocca endorsed tough trade legislation as part of his "competitiveness" package and complained that when he lobbied for a restrictive amendment to the House trade bill sponsored by Rep. Richard A. Gephardt (D-Mo.), "I learned that many red-blooded guys in Washington would rather be called a pervert than a protectionist."

Massachusetts Gov. Michael S. Dukakis (D), a rival of Gephardt for the presidential nomination and a critic of his trade legislation, told his fellow governors after Iacocca had finished his speech and departed that the Japanese and Korean trade policies Iacocca had criticized "were there seven, 10 and 20 years ago," and are not at the root of America's recently swelling trade deficits. Citing the budget deficits of recent years as the root cause of the trade deficits, Dukakis argued that "this is largely a government-made disaster."