Leadnow.ca and several other groups are urging their members to sign up as Liberal party supporters in order to promote the idea of electoral co-operation among progressive parties to ensure defeat of Prime Minister Stephen Harper's Conservatives.
Leadnow.ca boasts some 225,000 members, a huge pool of potential supporters for leadership contenders to tap into.
Since Murray is the only one of nine contenders to embrace co-operation, she is the most likely beneficiary of the advocacy groups' efforts.
Indeed, at least two online groups — Catch 22 Harper Conservatives and Fair Vote Canada — are openly encouraging their followers to support Murray.
Leadnow.ca's Jamie Biggar said his group is not endorsing any specific candidate.
However, he added: "At the moment, as Joyce is the only person in the race with a clear and strong position on co-operation, we do anticipate that the campaign will give her the most boost at this point."
The influence of online groups could be considerable.
Leadnow.ca and Avaaz, another online advocacy group with an even larger membership, undertook similar campaigns during last year's NDP contest. Long-shot contender Nathan Cullen, the only candidate in that race to support electoral co-operation, wound up placing a surprisingly strong third.
The two groups' combined campaigns resulted in some 10,000 people joining the NDP to support Cullen, Biggar estimated.
"Which we believe to be essentially unprecedented. (It's) evidence of the fact that there's a large constituency of people who really support this idea and want to get involved."
Online groups' influence could potentially be even greater in the Liberal contest, since no one need actually become a dues-paying, card-carrying party member to vote for the next leader. Anyone willing to sign up as a supporter of Liberal principles is entitled to cast a ballot.
And since the results in each riding are to be given equal weight, even a small surge in supporters in ridings with little existing Liberal presence could have disproportionate impact on the final outcome.
Still, it's unlikely the groups' efforts will derail front-runner Justin Trudeau's apparent juggernaut. Trudeau has flatly ruled out co-operation with the NDP or Greens.
Nevertheless, Biggar said the aim is to show all nine contenders there is an appetite for a more co-operative approach to politics and, over the longer term, to persuade opposition leaders they must join forces to end vote-splitting among progressive forces.
"Our objective is to show that people will get involved and vote for co-operation," he said.
"We don't expect to determine the outcome (of the leadership race). We do expect to influence the conversation."
Murray is proposing that Liberals, New Democrats and Greens hold run-off nominations to choose a single candidate to run in ridings won by the Conservatives last time with less than 50 per cent of the vote.
Her proposal is for one-time co-operation in the 2015 election, after which she is promising reform of the electoral system so that each party's share of the popular vote would be more accurately reflected in the House of Commons in future.
Although her eight rival contenders have adamantly rejected the idea, there is some evidence that rank-and-file Liberals may be more open to it.
Ron Hartling, president of the Liberal riding association in Kingston, Ont., wrote all candidates earlier this month to suggest they reconsider their rejection of co-operation in light of surprising support for the idea revealed during a recent membership renewal drive in his riding.
He attached an extract of a report from his association's outreach director, who found one-time members felt it was "arrogant" for most leadership contenders to reject the idea of co-operation out of hand, who blamed the Liberal party for the lack of co-operation to date and used words like "greedy," "power hungry" and "childish" to describe the party's stance.
In an interview, Hartling said the responses were gleaned from about 55 people who refused to renew their membership.
"It was totally unprompted and I was actually surprised at the number for whom (rejection of co-operation) was the reason," said Hartling, who is remaining neutral in the leadership contest.
"I thought that was relevant information for the candidates to consider, as opposed to locking themselves into being entirely negative on the subject."
The Liberal association in the Ottawa riding of Nepean-Carleton last month surveyed its members and supporters on options for ending vote-splitting. Of the 125 who responded, 72 per cent supported electoral co-operation with the NDP and Greens.
Another six per cent supported merger with the NDP and 20 per cent said no merger or co-operation under any circumstances.