The nation's governors yesterday ended their annual winter meeting by sidestepping the most controversial issue -- a call for a constitutional amendment requiring the federal government to balance its budget.

The governors, deeply divided on the issue, avoided bringing the matter to a vote. Instead, they passed, without debate, a resolution that reaffirmed a call for a balanced budget by 1981 and asked that President Carter appoint a committee to review the federal budgeting system.

The action was seen as a rebuke to California Gov. Edmund G. (Jerry) Brown Jr. and other governors who led a spirited defense of the balancedbudget amendment in earlier sessions of the National Governor's Association conference. It came at a late afternoon meeting without a whimper of protest from Brown, who wasn't present, or any other governor.

The only person to speak on the issue was Vermont Gov. Richard A. Snelling, a Republican, who had curtly thwarted attempts by Democrat Brown to expand the resolution in a committee meeting Monday.

Snelling, who headed the committee, said the resolution conforms with President Carter's pledge to balance the budget by fiscal 1981. "Rather than just issuing clarion calls," he said, governors decided to suggest specific areas where spending could be cut.

Meanwhile, the governors passed resolutions calling for federal policy on rural development and promotion of exports.

The group rejected a resolution, backed by sugar-producing states, that called for a minimum price of 17 cents per pound on domestically produced sugar. New Jersey Gov. Brendan T. Byrne argued "a guaranteed price of 17 cents is not in the interests of consumers."

The governors, ending a three-day meeting, gave a cool reception to the Carter administration's chief energy and inflation spokesmen. In the process, the governors, two Democratic congressional spokesmen and four Carter administration spokesmen expressed a growing frustration with the ability of government to do its job.

Perhaps the most telling moment of the day came when Edwin Edwards, the outspoken governor of Louisiana, asked Carter's chief inflation adviser, Alfred E. Kahn, how to explain to Louisiana teachers and public workers why they should accept a 7 percent wage increase when inflation is rising at a higher rate -- "bearing in mind I might want to run for reelection."

As part of his answer, Kahn said, "It's not part of my job to tell lies."

"It's a very big part of mine," replied Edwards.

The most extended, but inconclusive debate came over energy policy, with governors blaming federal officials for their problems and federal officials, in turn, blaming states.

"I think the most serious institutional problem we face is we can't get anything done in this country anymore," complained Sen. Henry M. Jackson (D-Wash.), who appeared on a panel with Energy Secretary James R. Schlesinger, and Rep. Morris K. Udall (D-Ariz.).