The state House of Representatives' expected formal approval today of Gov. Michael S. Dukakis's local aid package well end a week long challenge over a proposal that would make it easier for 11 cities-including Cambridge to delay Proposition 21/2 tax cuts.

For the cities hardest hit by the property tax cutting measure, the governor's plan would allow city councils, instead of voters, to approve spreading fiscal year 1984's required tax cuts over two years.

When Dukakis released his aid plan earlier this month. House leaders said they expected a smooth ride for the entire package. But last Tuesday, Republican opposition forced an amendment calling for a nonbinding rejection of the Prop 21/2 plan, charging that it would undermine the 1980 law.

The amendment narrowly passed, 73-70, forcing stunned House leaders to maneuver quickly for a reconsideration vote Wednesday. After heavy lobbying by Democratic leadership, the governor's office, and city representatives-including City. Manager Robert W. Healy-the House voted down the amendment, 78-68.

The House then passed a statement of intent to accept all of Dukakis' package, 13-32. The Senate had approved the entire plan formally last Tuesday, 20-14. Yesterday the House passed the first reading of the bill without attempting to amend it.

Opponents of the tax-cut delay criticized the final decision for changing Prop 21/2 without voter consent, but they still claimed success.

"We were astonished by our original victory," said Barbara Anderson, executive director of Citizens for Limited Taxation, the group that championed the measure in the 1980 referendum. She added that "we never thought we could hold it."

She predicted, though, that because of the publicity about the issue, city councils would be more concerned about taking advantage of the tax-cut change.

But with Cambridge unable to complete the on going property revaluation that would allow the city to maintain revenues while cutting taxes to Prop 21/2 levels. Cambridge probably would spread its required 15 percent property tax cut over two years, Richard C. Rossi, deputy city manager, said last week. He added that the change would only give the city more time to handle the tax cut, without changing the actual intent of Prop 21/2.

Anderson also contended that the tax-cut delay passed only because Wednesday's lobbying made legislators afraid of losing the rest of the substantial local and package.

State Rep. Saundra Graham (D-Cambridge), who also serves as a city councillor, acknowledged that "a deal was struck," but she defended the city council's control of the taxes.

"Cities should have the right at least to separate," she said, adding that the city council had proven that Cambridge was well managed.

An administration official who asked not to be identified, called the entire debate a minor part of the overall aid plan, although he admitted that "we wanted to win once it became a political issue." He added that the debate is really just a question of whether or not you believe in representative government.

With both branches formally accepting the governor's and package it will move through legislative steps until the state's entire budget for fiscal year 1984-beginning July 1-is passed.