At the White House last night, the nation's governors ate Cornish hen and little chocolate baskets filled with sherbet, listened to Pearl Bailey belt 'em out in the East Room and generally groused about the state of the economy.

But never, never to the president in his own home. Even the Democrats know that's taboo--no matter how bad life is outside Washington.

"I served in Congress and I don't know if a social occasion is the appropriate place to start complaining," said Michigan Gov. James Blanchard, a Democrat, whose state is being strangled by debts to the federal government, among other things. "We're having a horrendous problem with our deficit. We've borrowed a lot of money for unemployment compensation. Many states have . . . But this is a goodwill dinner. I think we'll save business for Monday morning."

The black-tie dinner kicked off the four-day winter meeting of the National Governors Conference, where the federal budget and deficit are the sore points.

In his toast to the governors, President Reagan addressed the nation's economic woes, but painted a rosy future.

"The year that passed since our last state dinner has been a trying one for each of us and for all Americans," he said. "Our economy suffered the debts of this recession. Many of our citizens lost their jobs and may find themselves in need of government support. Our budgets were strained and administrations tested. But by working together . . . we have weathered the worst of the storm. And now the economic recovery in America has begun."

Not everybody took the toast seriously.

"I'll tell you, when they were toasting, the only person I had eyes for was Chuck," said Lynda Bird Robb, wife of Virginia Democrat Charles S. Robb. They were married in the White House 15 years ago.

"I toasted him for our anniversary, a little late," she said.

"Yeah, when everybody was toasting cooperation, we just looked at each other," said Charles Robb.

Many of the governors in town are particularly concerned with the approximately $10 billion in federal loans that states currently owe for state unemployment compensation. Because recent loans to the states have carried a 10 percent interest charge, the debts some states have accrued have been crushing.

"Our interest alone is $160 million," said Ohio Gov. Richard Celeste, a Democrat. "We have a very serious problem with unemployment in Ohio."

"We've stuck our necks out pretty far with this debt," said Pennsylvania Republican Dick Thornburgh. "The economy is in bad shape, and the current law is imposing a penalty on states that have the highest unemployment. We have already made our case (on Capitol Hill), and Monday morning we'll make our case to the administration."

The governors are expected to meet with President Reagan at 9:45 this morning, before he flies to California to be with Queen Elizabeth II. Nancy Reagan left last Tuesday to begin her official hosting duties for the royal party.

The nearly 130 guests began arriving at the White House diplomatic entrance around 7:30 to the sweet sounds of harp music in the lobby. In addition to the governors, the list included Vice President and Barbara Bush, national security adviser William P. Clark, Energy Secretary Donald P. Hodel and Health and Human Services Secretary-designate Margaret Heckler. Heckler appeared to be the only woman not in floor-length attire. She wore poppy-colored culottes that fell right below the knee.

Dinner was served in the State Dining Room on the new Reagan china. Ivory brocade tablecloths and red tulips took the winter's edge off the evening.

After dinner, on the way in to the entertainment, Phyllis George Brown, wife of Kentucky's Democratic Gov. John Y. Brown, seemed to have misplaced her husband for a few minutes.

"Where's your husband?" asked Colorado's Richard D. Lamm, a Democrat.

"I thought he was with you," said Brown, a striking presence in white silk and diamonds.

"Well, when last seen he had his tape measure out in the other room and he was trying to see if his office couch would fit," said Lamm. They both laughed approvingly.