The main dissent, authored by Justice Charles Johnson, and joined by Justices Debra Stephens and Jim Johnson, focuses entirely on justiciability:
The majority hardly recognizes, let alone analyzes, that this court has been repeatedly asked to step in and decide this issue, and we have consistently held and rejected that invitation.
The dissent goes on for nine more pages, but their basic argument is: "What's changed? Fuck all, that's what!" Though not exactly in those words.
The majority responds by pointing out the absurdity of accepting the state's position that the supermajority requirement would only be justiciable if the legislature chose to ignore it:
Given that the legislator respondents cannot ignore the Supermajority Requirement without violating their obligation to uphold the laws of the state, the State's position would render the Supermajority Requirement unreviewable and is therefore unacceptable.
Damn straight. The notion that the constitutionality of a statute can only be justiciable in its violation is a recipe for undermining the rule of law.
In a separate dissent, Justice Jim Johnson does object to the majority opinion based on the merits, but Johnson's dissent reads like a Tea Party pamphlet, so it's really hard to make heads or tails of his arguments. Something about property rights and the The Federalist Papers. Or something. Regardless, that leaves only one out of nine justices on the record arguing that the supermajority requirement is constitutional on its merits. And that one justice is more than a little bit crazy. Which kinda tells you how weak the constitutional argument really is.