The option whether the proposed amendment shall be ratified by state legislatures or by state conventions is optional and entirely at the discretion of Congress.
No fair reading of either procedure gives Congress the option not to act but history tells us that Congress has played games with its obligation to call a convention of the states and there does not appear to be an explicit remedy for that breach of duty outlined in the Constitution.
The judicial branch would likely not touch it. However, what would prevent the states themselves from proceeding?
In any event, these obstacles are obstacles toward enacting amendments and most of the criticisms which we confront have to do with a runaway convention, a situation precisely the opposite.
