In addition to the grants otherwise authorized by this chapter, the Secretary is authorized to make a grant for the purpose of providing all or any portion of the required State or local share of the cost of any public works project for which financial assistance is authorized under any provision of State or local law requiring such contribution. Any grant made for a public works project under this section shall be made in such amount as may be necessary to provide the requested State or local share of the cost of such project. A grant shall be made under this section for either the State or local share of the cost of the project, but not both shares. No grant shall be made for a project under this section unless the share of the financial assistance for such project (other than the share with respect to which a grant is requested under this section) is immediately available for such project and construction of such project has not yet been initiated.