Where is this written?
If you read the state constitutions I'm sure you will find that acts of the legislature requires a majority vote. if a legislature is requesting the government to do, or not do something it should take a majority vote.
Which assumes the legislature has the power to request the vote be delayed to begin with. Every state has placed responsibility to running, elections, validating the votes, and submitting the count to the Electoral College to some state agency like the Secretary of State or Election Boards or what have you. Approval of their decision by the legislature is not required. Requesting the votes be held up should fall outside their ability as well. Unless they change the law. And that would certainly require a vote of the entire legislature.