No, the states can start the process too
Article Five of the United States Constitution describes the process whereby the federal Constitution may be altered. Amendment proposals may be adopted and sent to the states for ratification by either: OR By a Two-thirds (Supermajority) vote of a national convention called by Congress at the request of the legislatures of at least two-thirds (at present 34) of the states. Two-thirds (Supermajority) vote of members present—assuming that a quorum exists—in both the Senate and the House of Representatives of the United States Congress;
There is nothing more Scott Walker can do as governor.