That’s going a ways back for me. However, after refreshing my memory on this topic, I can tell you that this is false. All thirteen states had to be behind whatever amendment was being offered, and since that’s really all that could be done at the time, there was no provision for something in Congress if there weren’t enough votes.
I mean, think about it, this is the fledgling USA that doesn’t want to repeat the disaster that brought the revolutionary war around. They haven’t quite figured out a system to give a good balance between state and federal power yet.
Thankfully, they did solve this problem. It’s somewhat easier to amend the constitution, but it’s not much easier, as it requires three-quarters of the states and a couple of other things to be behind the amendment.