The group said it will return all funds to donors if Collins votes against Kavanaugh.
It looks as though all Senate Republicans will vote to confirm, with Vice President Mike Pence available if needed as a backup.
Collins is referring to a large-scale crowdfunding effort by which liberals have raised about a million dollars to influence her against Kavanaugh.
In a second voice mail, the caller calls Collins "a feckless, feckless, feckless woman standing there letting Trump and his appointees steal the right to choose what women do with their bodies".
Most senators' votes for or against Kavanaugh are foregone conclusions, but the Senate's two openly pro-abortion Republicans, Collins of ME and Lisa Murkowski of Alaska, could potentially sink his nomination.
The Maine's People's Alliance has banded together with the Mainers for Accountable Leadership and Ady Barkan, a dying father who has campaigned for healthcare reform, to ask Collins, a Republican senator from Maine, to vote no on Kavanaugh.
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She has previously voted against the Republican Party, most notably during the attempted repeal of the Affordable Care Act.
Adav Noti, a senior director at the nonpartisan Campaign Legal Center, which works on rules of ethics and finance in government, told The Washington Post that he thought the listing was illegal, noting that bribery is a federal crime.
"I always wait until after the hearings are complete before making a decision, and I'll do so in this case as well", she said.
"You have the chance to stand up for the people of ME - and for the entire country - by rejecting this Supreme Court nominee", the fundraising site reads.
NBC News reported on profanity-laced voicemails and letters Collins has received from activists who oppose Kavanaugh's confirmation. "Those are the people we're here to represent and those people get the bulk of our attention". But she also told reporters last week she thinks Kavanaugh will uphold the case because he told her it's considered "settled law".
Another Senate Democrat who voted for Gorsuch and is seeking reelection in 2018 is Indiana's Joe Donnelly. If all Democrats and left-leaning independents vote "no", it would take two Republicans voting against Kavanaugh to sink the nomination. During the 2014 campaign, where Collins bested her Democratic opponent, Shenna Bellows, by a 68 to 32 percent margin, Collins spent $5.5 million and Bellows spent $2.3 million.