If they succeed, they'll be boldly going where no political party has gone since 2004, when individual donations were dramatically restricted and corporate contributions banned.
Since those political fundraising reforms were implemented, the Conservative party has been the unrivalled king of the fundraising hill, routinely raking in two to four times more money each year than the Grits.
But the Liberals have been closing the gap since Justin Trudeau took the helm in April.
And, while they'll still fall well short of the Tories' total haul for 2013, they're aiming to at least bring in more donations than the ruling party over the last three months of the year.
An intensive 12-day fundraising campaign, which ended Friday, pulled in just over $1 million — a sum that Liberals calculated was necessary to ensure fourth quarter supremacy.
The campaign included pitches from former prime ministers Jean Chretien and Paul Martin, as well as Garneau, erstwhile astronaut and now a Liberal MP.
"If you give, you will be making history as I did when I thundered upwards into the heavens," Garneau said in an email, appealing to supporters to venture "into the unknown."
However, the Tories aren't about to cede the title of champion fundraisers without a fight.
Last week, they launched a "seize the moment" campaign, aimed at raising $2 million by year end.
"The success of our party over the last 10 years has been a result of our ability to consistently raise more money than our opposition," Conservative party president John Walsh said in an email blast to supporters.
"Justin Trudeau and the Liberals have made fundraising their top priority and they are working hard to close the gap. We cannot let that happen."
Liberal national director Jeremy Broadhurst acknowledged his party can't be absolutely certain that the "million dollars for change" campaign will vault the Liberals ahead of the Tories. The calculation that an additional $1 million would do the trick was based on what the Grits had already raised in October and November and "an educated projection based on past trends" of what the Conservatives were likely to raise over the same period, he said.
That suggests the Liberals are looking at a total of at least $5 million in the fourth quarter — which is what the Tories raised over the last three months of 2012.
"We have set ourselves a goal of trying to surpass the Conservatives in total amount raised in the fourth quarter," Broadhurst said.
"It's an ambitious goal — and something that we have not done in the new fundraising era — that we may not make this time. But it is crucial that we close that fundraising gap in order to level the playing field and this campaign was a key part of this effort."
In a "handwritten" thank you note from Trudeau, emailed to supporters on Sunday, the leader said the party didn't try to figure out if raising $1 million in 12 days was "doable."
"We just flat-out asked you to make something extraordinary happen - and you did."
Still, a fourth quarter fundraising victory won't be enough to vault the Grits ahead of the Conservatives for 2013 as a whole.
Financial reports filed with Elections Canada show that the Conservatives raised $12.8 million from January to the end of September. The Liberals raised $6.9 million and the NDP $4.5 million.
Both the Tories and the NDP were down slightly from the same period last year while the Liberals were up by $1.4 million.
Liberals are particularly pleased that, for the first time, they had more individual contributors than the Conservatives in both the second and third quarters this year — 38,000 and 30,000 respectively, compared to 30,400 and 29,000 for the Tories.
Indeed, the Liberals more than doubled the number of individual contributors in the first nine months of 2013 over the same period last year, while the Conservative and NDP numbers dropped slightly.
"I'm extremely proud of the kind of fundraising we're doing. We're reaching out to small donations," Trudeau said in an interview last week.
Contributors are not just giving money, he added; they're giving their time.
"We have developed a culture of volunteerism ... that we're incredibly proud of. We are drawing in people to make phone calls, to reach out, to go door to door, to organize, to be part of a political process at a time when cynicism has never been higher," Trudeau said.
"For me, money is a piece of it but recruiting volunteers is every bit as important, if not more."