If the Council finds, upon the opening of bids for a public improvement requiring the assessment of property specially benefited thereby, that the lowest responsible bid for such improvement substantially exceeds the engineer's estimate, it may, in its discretion, hold a special hearing of objections to proceeding with the improvement on the basis of such bid and may direct the City Recorder to publish, post, or mail reasonable notice thereof in the manner set forth in Section 3.12.040. (Ord. 2-1961 § 7, 1961.)