When President Reagan swept into the marble-columned House last night, wearing his Boy Scout smile and shaking every hand in sight, the roars and whistles of the crowd filled the domed chamber with triumphant music.

In the front row, black-robed justices of the Supreme Court mingled with gray-suited Cabinet members. Past presidential candidates from Barry M. Goldwater to Henry M. Jackson stood among the rows of senators. Representatives from Brooklyn to Los Angeles, diplomats from Greenland to Ghana -- all heads turned toward the president.

But once the speech was launched, its gloomy litany of inflation, debt and spending cuts clearly divided the chamber between the Republicans on Reagan's left, who jumped up to applaud at every opportunity, and the Democrats on his right, who sat grimfaced, their hands folded, during most of the speech.

At the end, when Reagan declared that his plan should be "our plan," everyone stood to show respect -- whether enthusiastically or merely politely -- except for eight black congressmen sitting in the fifth row. Blacks claim Reagan's spending cuts would affect them particularly serverly.

The mood of Republicans was euphoric. "This is a sea change of governmental philosophy," Indiana Sen. Richard G. Lugar said almost reverentially.

The Democrats pledged cooperation, although many of them are reluctant to see social programs sharply cut. "We don't have the votes, so we have to grit our teeth and cooperate," said Rep. William M. Brodhead (D-Mich.). "Reagan is popular and the country wants us to play ball with him. So we will -- until he fumbles."

But Reagan, speaking calmly from the podium, reading his notes methodically from 5 by 7 cards, was looking beyond the Lugars and Brodheads to a bank of television cameras poised like a small armada in the first row of the gallery in front of him.

"Reagan has Congress by the tail," said Rep. James Leach (R-Iowa). "The question in everyone's mind is how he interacts with their constituents -- how good he is at turning the presidency into a bully pulpit."

The realization that what appeared on national television last night was perhaps more real than what could be seen from a leather chair in the House chamber cause a few members to watch the event on television, too. "That's the way my constituents see it," said Rep. Richard Bolling (D-Mo.), chairman of the House Rules Committee, who watched the president at his home. He called Reagan's performance "workmanlike."

But if Reagan perceived any hostility from the right side of the chamber, he did not let on. The president beamed from ear to ear, gazed up appreciatively at his wife, sitting in the gallery in a dazzling red dress, and showed all of the self-confidence he is known for. It was his night -- a glittering affair of pomp and publicity. He had produced what he had promised: a drastic program for change.

The only problem left was to get it passed by Congress.