They heard good old down-home music like "Home on the Range" and "Carry Me Back to Old Virginny" and ate French cuisine a la Japanese. In between, they chewed on a generous helping of issues dominating their midwinter conference.

They were the nation's governors out on the town last night at the Japanese Embassy, where Ambassador and Mrs. Fumihiko Togo entertained them on the second night of the annual bipartisan governor's conference.

Kentucky's Gov. Julian M. Carroll could not let the occasion go by without a healthy dig at the administration and Congress, a tradition which the chairman of the National Governor's Association is expected to uphold.

"We have a good relationship with our central government," Carroll, a Democrat, told the crowd of several hundred as he led the responding toast, "but sometimes our friends here forget where their power came from. It takes only once a year."

The conference's focus on international trade generated the kind of enthusiasm last night one might expect to find among a group of people anxious to drum up business for the folks back home.

"They've spent a lot of time discussing the importance of trade," said presidential assistant Jack Watson, one of several top-level Carter advisers at the party.

Last night's Japanese connection seemed only natural to Carroll, who noted that after years of buying products made in Japan, Americans were now shipping items to Japan for purchase there. "The American people have no greater friend than our Japanese friends," 'he said.

The diplomatic guests included the chief of China's liaison office here, Ch'ai Tse-min, who offered no elaboration on the duration of the Chinese fighting in Vietnam other than an enigmatic, "I believe it won't be long."

When Edwina Dalton met Ch'ai, she told him that she and her husband, Virginia Gov. John N. Dalton, would be visiting China in June.

"I told him I wanted to be sure that that war is over," she said, adding that, "he just smiled."

Before dinner, guests were invited to witness a tea ceremony demonstration, but were politely asked to park their cocktails at the door. Most who watched the highly ritualistic ceremony came away impressed if also a little uncertain of its significance. One Senate wife mistakenly sat on a low table before she realized what it was. She beat a hasty retreat at the first opportunity.

Dinner was served at tables of 12 where the guests included David Brinkley, Roger Mudd, Carl Rowan and David Broder from the media; Sens. Charles Percy (R-Ill.), Harrison Williams (D-N.J.), Claiborne Pell (D-R.I.), Mark Hatfield (R-Ore.); presidential assistant Tim Kraft and U.S. trade negotiator Robert Strauss, from the administration; and such governors as Arkansas' 32-year-old Bill Clinton, Texas' William Clements and Illinois' James Thompson.

Nowhere in sight was California's Gov. Jerry Brown, who had been unable to mobilize support demanding that Congress balance the federal budget.

Even so, the issue had some believers at the party, including Oregon's Victor Atiyeh who said he was "shocked" that Congress has not reacted.

"Congress doesn't believe we're really going to do this," he added, saying that, "tonight we're social," but tomorrow he would be visiting his state's members of Congress on the Hill.

For a scary minute, Jeanette Williams thought she'd lost her heart -- a diamond pin her husband, Harrison, had given her for her birthday.

"After Mrs. Togo said that Attorney General Griffin Bell was going to frisk everybody," Mrs. Williams said, "a waiter found it on the floor."