"If the bombs fell in this room," President Ronald Reagan said to America's governors at the White House last night, "it would certainly be a strain on the country." Weak laughter.

The president was playing host and earnest suitor on a stage in the East Room, and from the looks of things, he gently won over some of the governors. In the candle-lit White House and Chandon Extra Dry bubbled away.

"I don't think this changes anybody's mind on specific issues," said Gov. Bruce Babbitt of Arizona, a Democrat, "but it's awfully important in the long run. I think it will pay back some dividends to the president."

But from a Republican, Virginia's John N. Dalton: "The resolution we passed backing his program had only two dissents, which represents the strength of the feelings by the governors that he's on the right track."

The black-tie dinner was the flattering windup to a two-day courtship organized for the governors by the president and his advisers. "Between us," the president had said earlier during his toast, "we are going to see America solve its problems and have the cooperation between you -- the chief executives of the states -- and the federal government that was created by the states."

On the economic situation, Reagan advised them to look for some changes. "What we're trying to do is alter the economic situation with one word, from economic control by government to economic control on government."

This week, the president had the governors in for a 90-minutes meeting to explain his budget cuts, and at the same time, promote the non-earmarked block grants he wants to send to the states. It's all a part of the governors' annual winter meeting here, a meeting in which they gave qualified backing to Reagan's cuts but also went to a dazzling number of breakfasts and receptions.

Last night was the snazziest of those. As a delicate harp played, governors and their spouses arrived in all colors, sizes and shapes. Sequins were popular, and so was red. Phyllis George, the wife of Kentucky Gov. John Y. Brown, wore a revealing red dress that caused photographers to ask her to pose for pictures.

"I'll give her a big hug," said the governor, cozying up for the camera.

"If he can get his arms around me," responded his wife. Once she was thin, then she got less thin, and now she's in between.

The Reagans waited upstairs in the family quarters for all their guests to arrive before descending the Grand Staircase. The U.S. Marine band played "Ruffles and Flourishes." When they arrived at the bottom of the staircase, they stopped, waved and smiled for photographers before proceeding on to the East Room to the tune of "Hail to the Chief."

The president's cheeks were so pink he looked like he'd been on vacation at a mountain ranch in California. He had. His wife was wearing a brown chiffon Bill Blass dress with a cream-colored silk rose at her bosom. Around her neck were three strands of pearls and in her ears, pearl-and-diamond drop earrings.

When toasting the governors, Reagan mentioned that an 11-year-old boy had written him a letter. The boy, the president said, predicted "a few more gray hairs on your wise old head." The governors chortled. "Just go to the office," the president continued to quote from the letter. "Be happy you're only president -- and don't have to be God."

Over coffee and liqueurs in the state rooms where fires crackled, the governors talked about what the budget cuts would mean.

From Maryland's Harry Hughes, a Democrat: "I agree the goals are good -- I would reserve my judgment on individual parts of it." For starters, he said, these include the Appalachian Regional Commission, Medicare and mass transit.

From Illinois' James Thompson, a Republican whose state could lose as much as $525 million in federal funding if the cuts are approved: "If you don't stand up and say you'll take budget cuts of that magnitude, you can't get any cuts done. You've got to share the pain."

And from Brendan Byrne, the New Jersey Democrat: "You can't be mad until we see what happens in the Congress. Right now, I'm nervous."

The after-dinner entertainment was a mini-performance of the Broadway musical "A Chorus Line." Reagan clearly loved it, and after the show went up on the small East Room stage to shake hands with all 26 of the cast members. "I wish I'd started out in show business," he joked.

And then there was dancing and champagne. About half the crowd danced, including the Reagans. They swished around on the marble floor of the Great Hall to the tune of "Will I Take My Sugar to Tea?"

Guests of President and Mrs. Reagan at last night's White House dinner : Gov. Lamar Alexander (R-Tenn.) and Mrs. Alexander Gov. George Ariyoshi (D-Hawaii) and Mrs. Ariyoshi Gov. Victor Atiyeh (R-ore.) and Mrs. Atiyeh Gov. Bruce Babbitt (D-Ariz.) and Mrs. Babbitt James A. Baker III, chief of staff, and Mrs. Baker Secretary of Commerce Malcolm Baldridge and Mrs. Baldridge Gov. Christopher Bond (R-Mo.) and Mrs. Bond Gov. Joseph E. Brennan (D-Maine) Gov. John Y. Brown (D-Ky.) and Mrs. Brown Gov. George Busbee (D-Ga.) and Mrs. Busbee Vice President and Mrs. Bush Gov. Brennan T. Byrne (D-N.J.) and Mrs. Byrne Joseph W. Canzeri, deputy assistant to the president Gov. John W. Carlin (D-Kan.) William J. Casey, director of Central Intelligence Gov. William P. Clements Jr. (R-Tex.) and Mrs. Clements Gov. John N. Dalton (R-Va.) and Mrs. Dalton Michael K. Deaver, deputy chief of staff, and Mrs. Deaver Gov. Lee S. Dreyfus (R-Wis.) and Mrs. Dreyfus Gov. Pierre S. duPont IV (R-Del.) and Mrs. duPont Secretary of Energy James Edwards and Mrs. Edwards Gov. John V. Evans (D-Idaho) and Mrs. Evans Stephen B. Farber, executive director, National Governor's Association, and Mrs. Farber Gov. Hugh Gallen (D-N.H.) and Mrs. Gallen Gov. J. Joseph Garrahy (D-R.I.) and Mrs. Garrahy Gov. Jay S. Hammond (R-Alaska) and Mrs. Hammond Gov. Harry R. Hughes (D-Md.) and Mrs. Hughes Gov. James B. Hunt Jr. (D-N.C.) and Mrs. Hunt Gov. Bruce King (D-N.M.) and Mrs. King Gov. Edward J. King (D-Mass.) and Mrs. King Gov. Richard D. Lamm (D-Colo.) and Mrs. Lamm Gov. Robert F. List (R-Nev.) and Mrs. List Gov. Juan Luis (I-V.I.) Gov. Scott M. Matheson (D-Utah) and Mrs. Matheson Peter McCoy, deputy assistant to the president and director of staff for the first lady, and Mrs. McCoy Edwin Meese III, counselor to the president, and Mrs. Meese Gov. William G. Milliken (R-Mich.) and Mrs. Milliken Gov. George Nigh (D-Okla.) and Mrs. Nigh Gov. Allen Olson (R-N.D.) and Mrs. Olson Gov. William O'Neill (D-Conn.) and Mrs. O'Neill Gov. Robert D. Orr (R-Ind.) and Mrs. Orr Joseph Papp, producer, and Mrs. Papp Gov. Albert Quie (R-Minn.) and Mrs. Quie Gov. Robert D. Ray (R-Iowa) and Mrs. Ray Secretary of the Treasury Donald Regan and Mrs. Regan Gov. Richard W. Riley (D-S.C.) and Mrs. Riley Gov. John D. Rockefeller IV (D-W.Va.) and Mrs. Rockefeller Edward J. Rollins, deputy assistant to the president for political affairs Gov. Carlos Romero-Barcelo (Puerto Rico) and Mrs. Romero-Barcelo Gov. Ted Schwinden (D-Mont.) Gov. Richard A. Snelling (R-Vt.) and Mrs. Snelling Gov. John Spellman (R-Wash.) and Mrs. Spellman Gov. James R. Thompson (R-Ill.) and Mrs. Thompson Gov. Charles Thone (R-Neb.) and Mrs. Thone Gov. Richard L. Thornburgh (R-Pa.) and Mrs. Thornburgh Gov. David C. Treen (R-La.) and Mrs. Treen Gov. Frank D. White (R-Ark.) and Mrs. White Richard S. Williamson, assistant to the president for intergovernmental affairs Gov. William Winter (D-Miss.) and Mrs. Winter