Americans are now much more inclined to have Washington give financial help to cities than they were two years ago when New York teetered in the edge of bankruptcy.

An 8 1/2-to-14 per cent majority feels it is at least somewhat important that cities with financial problems be federally subsidized - up from the 68-to-26 per cent who felt that way in 1975. Suburban and big-city residents are more supportive of such federal aid than are small-town and rural dwellers.

The finding of the latest Harris survey of 1,540 adults suggest a growing concern throughout the country for the plight of the cities. Seventy per cent of the public feels that the financial crisis facing the cities is "very serious" indeed.

A 89-to-5 per cent majority feels that "cities are the center of business, communications, and the arts, and must be made better places to live in.

A 77-to-14 per cent majority agress that "America cannot survive unless the problems of the cities are worked out."

An 84-to-9 per cent majority feels that "slum housing in the cities should be renovated and fixed up so those building are livable again."

A 55-to-27 per cent majority feels that "if we neglect the cities, we will have a racial explosion on our hands." This is a fear that has dwidled since the riot torn 1960s, when a 68-to-19 per cent majority felt that way.

Despite this general sympathy for the cities, the public is still doubtful about certain aspects of urban life:

A 67-to-24 per cent majority believes that "cities are full of crime and corruption and people who want a handout."

Although 43 per cent disagree, 40 per cent agree with the assessment that "even if the poor are given clean, new homes, they will make them dirty."

Only a very narrow 45-to-43 per cent plurality rejects the charge that "it is just about impossible to control air pollution in the cities."

A 57-to-31 per cent majority rejects the claim that "big cities are unmanageable and money spent on them is wasted.

A 51-10-33 per cent majority does not believe that "money spent on welfare in cities is just wasted and doesn't really help anyone."

And by 58-to-29 per cent, a solid majority disagrees that "giving money to the cities is just another way of giving money to blacks and other ethnic minorities."