Yeah, I can see the Mitch McConnells, John McCains, and Thad Chochrans of the world voting for this one. There are 14 senators running this year for their third term or higher. Term limits would force them to go back to the sticks and work for a living.
Read your Constitution. Under Article 5, the states would form a convention to propose amendments. The amendments would need to be approved by 3/4 of the states to be ratified. Nowhere in this process does Congress get to vote on it. This procedure was put in place to give states a mechanism to reign in Federal power. Nobody in the Federal government plays a part in this type of amendment process.