There has LONG been a SENATE RULE requiring 21 of 31 votes for a bill to be taken up OUT OF ORDER. Presumedly this rule COULD be changed by THIS, or any other, senate. I am unaware of ANY such house rule and would appreciate a cite if anyone has the time.
The 21 of 31 is not a Senate Rule it is a Lt Governor ploy. The power of the Lt Governor comes not so much from the Constitution as it does the Rose Bush Debate that opened every session for the last 40 years, and accounts for the 2/3 vote needed to bring something up.
In talking to the two Reps last week they were convinced that to revisit re-districting they would need a two thirds vote in each house. I have no further information.