On Sunday, Cummins gave dissidents within the party until noon Wednesday to get in line or resign their membership.
Ariane Eckardt, president of the party's Burnaby North Constituency Association, worries the ultimatum will only divide the party further.
"It's not the party we disagree with,” Eckardt said. “We disagree with the leader. It's the party we'd like to save."
Political scientist Hamish Telford says the move reminds him of another political leader.
"What really struck me is the authoritarian tone … This is a North Korea kind of thing right, you know Kim Jong Il and demanding personal loyalty to the leader. This is very unusual," Telford said.
'Subversion of the democratic process'
But Cummins supporter and party president Al Siebring defended the move.
"We have these constituency association presidents who are calling for a leadership review — it’s a subversion of the democratic process," he said.
"The party has spoken. If these people are not willing to live with the results of a democratic process then do the honourable thing and go someplace else."
Cummins's leadership of the party has come into question in recent months.
A push to oust Cummins, led by party vice-president Ben Besler, failed last month as 70 per cent of party members voted against holding a leadership review.
Siebring calls the internal conflict a distraction from the upcoming election.
"Do I want these people to leave? No. I want them to respect the democratic process, come back into the party and work with us," he said.
"If they're not prepared to do that, if they're that upset about Mr. Cummins, this is not the party to be in. It's really quite that simple."
The party's political fortunes have also been on a downward slide with the recent defection of candidate John Martin and the resignation of John van Dongen, the party’s only sitting MLA.
The party says it will make the public the number of party members who have decided to resign on Wednesday.