The resolution providing for the construction or reconstruction of a sidewalk shall give the owner of the abutting property not less than thirty days nor more than sixty days after its publication in which to construct or cause to be constructed or reconstructed the sidewalk at his or her own expense. Such resolution shall be published once in the official city paper, or if none, then in a paper of general circulation in the city. If the sidewalk is not constructed by the property owner within the time specified, the governing body shall cause the work to be done by contract.