"I think political parties, they're private groups, I think they have the right to put their candidate on the ballot the way they want," Jenkins said.
Taxpayers currently pay for party primaries, at a cost of about $3 million per statewide election, which has been used to justify setting rules for the party nominating process.
Count My Vote organizers argue the caucus system produces nominees that skew to the extremes of both parties and drive down voter participation.
If Jenkins' proposal makes it onto the November ballot and is approved by voters he said it would trump the Count My Vote initiative, because it changes the Constitution.
It is one of two pieces of legislation that would essentially nullify the Count My Vote initiative. SB54, which has passed the Senate, lets parties avoid the primaries in Count My Vote if the parties abide by requirements for absentee voting at caucuses and conventions, require 65 percent of delegate support to clinch the nomination instead of the current level of 60 percent and open primaries to unaffiliated voters.
Jenkins' proposal was approved 4-1 Wednesday by the Senate Government Operations Committee.
If it gets two-thirds support in both the Senate and House, it would go on the November ballot for voter approval.