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“I’m confident,” he said, “we’ll have a certified solution by Tuesday.”

The council also debated the best way to maintain funding for the Housing Production Trust Fund, which sets money aside to create affordable housing units in the city.

Mr. Evans said the fund has been “raided” each year to fund the city’s rent-supplement program.

“It’s a charade,” he said.

Council member Michael A. Brown, at-large independent, said on Tuesday he will reintroduce his plan to use funds from a pool of about $20 million in fiscal 2012 funds to compensate city workers for two of the four furlough days they took in 2011 — the two other days would be paid once revised revenue estimates arrive in June — and place the balance of the funds in the Housing Production Trust Fund.

Some council members object to the plan because they want to immediately compensate city workers for all four days.