Lieutenant Governor Timothy Murray’s office announced that Medford planners could count on up to $2 million in state infrastructure money if the City Council votes to approve plans to construct a 200-space parking garage in Medford Square. The announcement was made during an appearance by Murray at the Medford Chamber of Commerce luncheon Wednesday, said Murray spokeswoman Lauren Jones. The garage, part of a $30 million capital improvement project now under consideration by the council, is slated to cost about $8 million. But the state’s offer reduces Medford’s burden to $6 million, passing the onus to the councilors to agree to the city’s share. Some of them have argued that the city, under the direction of Mayor Michael J. McGlynn, failed to properly gauge the need for the 200-space structure. Councilor Michael Marks, who participated in a task force to examine parking in the square, has said without adequate enforcement, the city would have difficulty paying for the cost of the garage through parking revenues alone. - Matt Byrne