Ronald Reagan has said he admires Calvin Coolidge, and last week he proved that Coolidge's most famous political action -- there were not many -- still stirs a deep response among Americans. "There is no right to strike against the public safety by anybody, anywhere, any time," Coolidge told the striking Boston policemen, in the statement that made him a national political figure after World War I.

The reaction to Reagan's swift response to the air controllers' walkout was no less approving across the country than that accorded Coolidge long ago. Many who travelled by air last week were struck by the vehemence of the public comments.

"They ought to shoot them," one passenger told another at Washington's National Airport. They were the government, them the controllers.

By his handling of his first domestic crisis, the controllers' strike, the president has strengthened his already overpowering public position. He was firm, he was decisive, and he was right.

This doesn't mean he escapes unscathed from this episode. A glimmer of a harsher Reagan emerges, raising questions about how well he will deal with inevitable confrontations to come, whether at home or abroad. And certainly long-term economic and political consequences flow from this strike.

But there's no doubt that the strong public expressions expose genuine hostility toward this union, and unions in general. Nor should there be any misreading of what this public resentment represents, in political terms, for the president. He has seized an opportunity to show he can deal as effectively with confrontational union politics as he has with the Congress.

And the air controllers gave him a great assist. Their strike was illegal, their actions did violate their public trust -- and public oath.

Reagan demonstrates what effective presidents instinctively know: that the public always backs them when they take a strong stand on clear-cut public interest issues. Some history.

Harry Truman had reached the low point of his presidency in the wave of strikes that followed the end of World War Ii. He faced a crisis when a walkout of the nation's coal miners was followed by plans for a national rail strike, threatening to bring America to a standstill. As William Manchester writes, in his brilliant narrative history, The Glory and the Dream :

"The leaders of the two unions had long been allies of the Democratic Party, and when Truman called them to the White House three days before the strike deadline and offered generous arbitration awards, he expected them to accept. Instead they shook their heads stubbornly.

"'If you think I'm going to sit here and let you tie up this whole country,' he said, 'you're crazy as hell.'

"'We've got to go through with it, Mr. President,' one of them replied, 'our men are demanding it.'

"Truman rose. 'All right,' he said. 'I'm going to give you the gun. You've got just 48 hours -- until Friday at this time -- to reach a settlement. If you don't, I'm going to take over the railroads in the name of the government.'"

The deadline passed without compliance. Truman seized the railroads, went before Congress, asked for and got authority to draft into the Army all railroad workers, regardless of their personal situation. The unions caved. The rail strike never occurred. Leonine old John L. Lewis, the mine union leader who had loudly boasted, "You can't mine coal with bayonets," was forced to capitulate. He ordered his men back to work. Truman's popularity soared. So did his presidential authority.

As always, there's another side.

Not all the words last week were that supportive of the president. A friend tells of a conversation with a cab driver at Chicago's O'Hare Airport. "Well," the cabbie said, when asked what he thought about the strike, "the baseball people signed last week, and they're getting a lot of money. It appears to me the controllers are a whole lot more important to the public than baseball players. They're asking a lot less and if they make errors it hurts the public a lot more."

The public, more than the government and the union, represents the real other side of this episode. From that perspective, the president's actions are not entirely reassuring.

From the beginning of his presidency, Reagan's greatest strength as a political leader has been his ability to lift the country's spirits. He practices the politics of hope. His personality, his message, his appeal, all are bound up in restoring a sense of optimism to a country that has experienced years of self-doubt and serious internal divisions.

For the first time as president, he has displayed another, less attractive side. Firmness is fine in a president; indeed, it is desirable. But something else came through last week -- a harsh, unyielding, almost vengeful and mean-spirited air of crushing opponents. It makes you wonder how he will respond if faced with a direct, and dnagerous, foreign challenge, one rquiring the most delicate and skillful combination of strength and diplomacy. It also makes you wonder how he will respond when other American groups oppose him, as inevitably they will.

Perhaps it's unfair, but one gets the impression the prime objective of the administration is to show how tough it is, how it can break a union, however misguided and wrong that group may be. What has been lacking the administration is a sense that greater public interest questions are at stake here. Surely the objective should be something more than how best to get rid of 12,000 federal employes. The primary question should be how to get both sides together in the public interest, to moderate differences, to listen to grievances, to seek solutions, to examine ways to fashion the safest air system possible.

That approach appears to be missing in this struggle.

The issue is not presidential strnegth or weakness, but wisdom. Machiavelli's old prescription for great leaders -- that they must employ the characteristics of both the lion and the fox -- remains as relevant as ever. A dash of compassion, a display of a generosity of spirit, are also welcome, but absent now.

So while the president clearly has strnegthened his public standing for the time being, it's hard not to entertain a plauge-on-both-your-houses attitude over this domestic situation.