City Councilor Barbara Ackermann said yesterday she is considering running against incumbent Michael S. Dukakis for the 1978 Democratic nomination for governor.

"I am trying to assess the degree of disaffection with Dukakis, and so far there is a lot," Ackermann said yesterday.

The 52-year-old councilor stressed that Dukakis's fiscal conservatism has hurt the cities and towns of Massachusetts as well as the citizens of the state. "There is no question that local education and public hospitals have suffered because of Dukakis's balanced budget," she said.

Ackermann said she objects to Dukakis's policy of saving money by cutting medical payments to the poor and handicapped. "They still need the money and services--the poor have suffered for several years under Dukakis," she said.

Tax relief for property owners, unemployment and elderly services are also issues which Ackermann feels that the current administration has ignored.

Ackermann, a former mayor of Cambridge, was defeated for her council seat this fall. She has been on the council since 1962.

A member of the progressive Cambridge Convention '77 slate, she has been associated with many liberal movements including the 1968 presidential campaign of Eugene McCarthy.

Cambridge State Rep. Saundra Graham, a colleague of Ackermann on the City Council, said yesterday, "I do not think that she is anyone to fluff off. I would support her absolutely."

Graham, who also took issue with Dukakis's fiscal policy, said, "Ackermann has a tough battle ahead of her but with a lot of hard work her chances are good."

State Rep. Barney Frank '61, a frequent critic of Dukakis, yesterday called Ackermann an attractive candidate. "I'd love to see her as governor," he said. "However, a liberal candidate for governor needs to start immediately," Frank said.

Ackermann said she would continue to investigate how people feel about Dukakis. She plans to make a final decision on her candidacy within two months.

Although Ackermann acknowledges that Dukakis and Senate President Kevin Harrington, another potential candidate, would be difficult to defeat, she feels that "There is a large enough progressive vote to make a liberal electable."

The primary election will be next September.