The proposed resolution of intention shall be submitted to the legislative bodies which have jurisdiction over the territory into which the proposed work or the assessment district therefor may extend. When the resolution of intention is approved and the consent of the legislative bodies whose consent is necessary is obtained to the work and the formation of the assessment district described therein, the resolution of intention may be adopted. The consent if any shall, of itself, constitute assent to the assumption of jurisdiction thereover for all purposes of the proceeding and authorize the legislative body initiating the proceeding to take each and every step required for or suitable for the consummation of the work extending outside the limits of the city, and the levying, collecting and enforcement of the assessments to cover the expenses thereof and the issuance and enforcement of bonds to represent unpaid assessments.