Walking through the Des Moines, Iowa, airport the morning after the candidates' debate, John Anderson felt a new sensation. Strangers recognized him. They called his name. He was John Anderson, not John Nobody.

Until then, anonymity had been a tougher opponent than Reagan, Connally or the others. But suddenly, Anderson had in his hands for the first time the raw material of a presidential campaign: recognition. It was deserved. In the debate the night before, Anderson had confirmed the positive rumors: He is a man with a lively mind, his beliefs have foundation in something firmer than the passing public mood, and his sorties from the conventional path have led him to fresh ideas.

Anderson separated himself from the others in the debate in several ways. He was the only one with the backbone a nd humility to be specific in answering a pointed question about past mistakes.He was the only one not to toady before the Iowa farmers by attacking the president's partial grain embargo. On the energy issue, he trusted Iowans to have the intelligence to go beyond code words and perceive the sense in his 50 cent-a-gallon gas tax.

In another revealing moment, Anderson alluded to the thinking of C. Vann Woodward, the esteemed American historian. Only one other panelist was spry enough to drop in a learned quotation. That was George Bush. His wise counsel? Yogi Berra. In fact, Bush thought so much of Berra's wisdom about the nature of "wrong mistakes" that he alluded to it twice, as though Yogi was Shakespeare and Iowans, being simple country folk, needed a second interpretation.

In appearing before a national audience as the candid and thoughtful politician that his colleagues in Congress have long known him to be, Anderson moved forward. But he still needs some breaks. His new-found celebrity may not mean much in the caucuses on Jan. 21. He has lacked the money for the expensive organizing demanded by the caucuses. That means he hasn't been able to stroke Iowans the way to which they have become accustomed. The pampering is such that to get them out on caucus evening, they want at least a half-dozen personal phone calls from a candidate, an inscribed picture for the den and a promise to spend the night in the Lincoln Room of the White House.

Instead of getting into big-dollar and no-win competition with the Reagan, Bush and Connally machines in Iowa, Anderson has been campaigning mostly in New Hampshire, Massachusetts, Wisconsin and Illinois. In those states, he must win votes. In Iowa, his hope was to shine in the debate and win a few friends.

That he had done. If anyone would understand Anderson's predicament, it is Iowans. He is in the state to plant seeds, coming on as the patient farmer. The only question is whether or not the Republican regulars have the breadth to appreciate a man who is obviously trying to shake up a stagnant party.

Aside from restless Republicans, Anderson's appeal is to Independents and Democrats, none of whom will be in his caucus rooms Jan. 21. "Right now," Anderson said the day after the Des Moines debate, "I'd be heartened by a little bonus in Iowa. I have a good feeling going into the caucuses, particularly because during the debate I was able to reach out to citizens on the basis that it's time to discard the old politics."

Anderson didn't specify what would signify a "little bonus." With no paid workers in the state, he is in a position to get a thrust forward by only a modest showing. With Iowa being a monumentus state, and Anderson not in motion in any perceptible way before the debate, merely a sign of acceleration would be a victory.

It's an odd way to become president, except that Anderson is already comfortable with oddness. He is a Republican with progressive votes in civil rights, human rights, reaching out to the poor and hungry, as well as thinking twice about new commitments to unneeded weapons.

As delighted as he was in being greeted by people in the Des Moines airport, Anderson had another elation last Sunday. When he left the plane, in Chicago, he went through the crowds there as a new face.