With the party hoping to regain its equilibrium following a difficult spring, several Tory sources tell The Canadian Press that Harper would like the matter dispatched quickly.
But support for moving the leadership rules closer to a one-member, one-vote system appears to be centred in Harper's home province of Alberta.
Currently, leadership votes give each riding equal weight, no matter how many individual party members it has. It's a principle that Progressive Conservatives insisted on before merging with the Canadian Alliance to form the Conservative Party of Canada.
One of the resolutions that would change the party's voting rules comes from the riding of Wildrose. Peggy Strankman, president of that Conservative riding association, says she hopes for a healthy debate.
"The leadership rules are something that have come up in the past and people seem interested in discussing it to see if we can find an arrangement that everyone can support," said Strankman.
A system that would give larger ridings more of a say in a leadership vote is also appealing in Rob Anders' Calgary riding, where the MP says membership has reached 4,400. His riding association has endorsed one of the two resolutions to alter the rules.
"If every single riding association in the country has (the same say) there's no incentive for a riding association with 4,000 members to increase in membership and no incentive for a riding association that has 100 members to increase in membership," said Anders.
But Defence Minister Peter MacKay and others make the opposite argument. MacKay has argued that giving large ridings — many of them in the West — a bigger voice in a leadership race, would just marginalize and discourage Quebec, Atlantic Canada and other areas with fewer members.
Leadership candidates need to seek support across the country to achieve victory under the current system, MacKay has said.
"Nobody can describe it as a unifying issue," MacKay said of the debate. "It’s divisive. It pulls at old affiliations and old fault lines and I don't think we need that."
But things aren't exactly a cut-and-dry, East-West split or Canadian Alliance versus Progressive Conservatives split, Conservatives caution.
Harper himself is said to favour the current system, which he used to win the leadership in 2004.
Longtime Calgary MP Deepak Obhrai says he, too, supports the status quo.
"As far as I'm concerned, and I've been very clear on this issue, the past arrangement has worked very well for us and I don't see a need to change it," said Obhrai.
Still, there is a strong tradition on the Canadian Alliance/Reform side of the Conservative family for grassroots members to have vigorous convention floor debates on rules and policies.
"In a democratic society, I think one of our strengths is the ability to put ideas forward and have the opportunity to discuss them," said Strankman.
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