If this is New York's finest hour, as Mayor Edward Koch proclaims, he leaves no doubt who he has in mind for the Churchill role.

As London survived the Luftwaffe, he vows, so New York shall survive the transit workers.

Since the first morning of the nine-day-old strike, Koch has put on an extraordinary performance. He seems to be on the radio around the clock, making announcements, hectoring the strikers, giving advice on everything from how to keep a car radiator from boiling over to where to buy bargain theater tickets.

Koch has made himself a symbol of resistance to the strike. He turns up among crowds of commuters as they walk and bicycle to work, sometimes wearing a blue coach's windbreaker bearing the word "Mayor."

He is a cheerleader as well as coach in his efforts to keep his team's spirits up. "New Yorkers are best in adversity," he tells them.

"Don't give in," the faithful tell their leader.

Their words, Koch said in an interview, "restore my faith and my courage."

The Koch style is one part fatherly encouragement, one part wisecrack and one part stern law-and-order lecture. The mixture was brewed long ago, but it has never been so visible as during the strike.

Koch never had a second though about what his role should be. It never occurred to him to let City Hall assistants stand up front when questions arose about emergency traffic plans or special parking regulations.

He picked up the ever-present city Hall press corps with a thicket of microphones and headed out to slay the two evil dragons -- the Transport Workers Union dragon asking for wages the city cannot afford and the "gridlock" dragon. A gridlock is the ultimate traffic jam in which hundreds of thousands of cars lock themselves into the city's streets so that nothing can move.

"My job is to encourage people," Koch said of his 18-hour days of dragon fighting. He speaks often of his direct contact with the people and of suffering their troubles with them.

It is a high-risk act.

For the first nine days most of the people seem to be with Koch, but there are also many who grumble that he could use his time better by going to the bargaining table than by greeting commuters on the Brooklyn Bridge. The strikers and their sympathizers already see Koch as the enemy.

It could change," Koch said. "Your popularity can be lost in 24 hours. But then you can get it back in 24 hours."

If foot-weary or traffic-wery New Yorkers turn to anger, they will turn on the mayor, but Koch believes he is right and that he can keep most New Yorkers on his side despite their sufferings during the strike.

The message he wants to spread is that strikes by public employes are illegal under New York law and that the subway workers are paid reasonably well compared to other New York workers. "Nobody is well off," Koch said, "but the [Transit workers] are better off than the average New Yorker."

Under his two predecessors, John Lindsay and Abraham Beame, "the unions owned this city," Koch said. "Remember how Lindsay gave away the city?" Koch is fond of asking in what he quickly adds is not a personal attack.

Koch began today by telling the city at his regular morning briefing that this would be the worst day so far. The Wednesday after Easter is the second heaviest traffic of the year, next to the Wednesday after Christmas, he said. In addition, it was raining and public schools reopened today after spring vacation.

Traffic was awful. The rain lasted all day. But the city's emergency traffic patterns and heavy use of police to direct traffic kept the gridlock away for another day.

"We'll look back on today as one of the days that tested us and that we came through," Koch said in the morning briefing, which is carried live on at least two radio stations.

Koch believes tht Fiorello LaGuardia was the best mayor New York ever had and he wants to be judged against LaGuardia's standard.

LaGuardia's times were similar to the present, Koch said. There were labor and financial problems. The economy was staggering.

Koch has no doubt LaGuardia would be doing the same things he has been doing during the transit strike. After all, LaGuardia sold milk on the streets to demonstrate his position during a milk strike.