The Council shall have power by ordinance to provide for the construction, reconstruction, repair and maintenance by contract or directly by the employment of labor, of all things in the nature of all public improvements and to provide for the payment of any part of the cost of any such improvement by levying and collecting special assessments upon abutting adjacent and contiguous or other specially benefited property.  The amount assessed against the property specially benefited to pay for such local improvements shall not exceed the amount of benefits accruing to such property.  Any cost for such improvement in excess of any sum assessed therefor shall be paid by the City.