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The proposed amendment would need three-fifths support from lawmakers — 85 votes in the House and 29 in the Senate. If passed, the bill would then be put to a 2012 referendum.

Mr. Dwyer acknowledged gathering the votes on the floor or even in committee will be a tall task, but he said he thinks the amendment deserves to be put before the public.

“This place is a place of miracles. Strange things happen,” he said. “All we’re doing by passing my bill is saying that the public gets a right to vote on it.”