The appeal also invited the senator's backers to donate to either him, a group of other Democratic senators, or both.
"We depend on the help of grassroots supporters like you to be able to continue working for common sense solutions," a message on the fundraising site said.
The fundraising effort comes as Senate Democrats and the White House, which is preparing for its fifth State of the Union address, are undertaking a legislative push on income inequality, focusing on the real-world plight of voters adversely affected by the expiration of the benefits.
But the effort also underscores that aside from the legislative component, Senate Democrats are pursuing a political approach, asking voters to back their effort, not just by sharing their stories, but also by offering their financial support.
It's an issue, say some Democrats, that hits a figurative sweet spot—solving a policy issue that Democrats feel strongly about, but also buoying the party politically.
"I think the president sees it as a win-win," said former Democratic Rep. Vic Fazio. "Either you get what you ask for or you have an issue that will prove helpful."
The bipartisan legislation, sponsored by Sens. Jack Reed, D-R.I., and Dean Heller, R-Nev., also has the support of the Obama administration, but the measure foundered before Congress went on recess, with Republicans, angry that Majority Leader Harry Reid barred their amendments, blocking the measure.
Reid plans to bring the issue up again soon, with bipartisan talks going on behind the scenes, lawmakers say.
While Democrats are seeking campaign cash on the issue, Republicans working with Reed to advance the legislation say Democrats are still working in good faith to find a way to pay for the nearly $6.5 billion legislation.
"I was concerned that perhaps this was going to turn into one of these political issues, where each side uses it against the other, and that's not what I'm seeing," said Sen. Susan Collins, R-Maine, who has been working to forge a bill that can pass the Senate. "I'm seeing realistic, genuine discussions to try to find a solution."
The fundraising effort had the backing of a handful of Democratic senators, some up for reelection this year like Coons, Mark Warner of Virginia, and Mark Pryor of Arkansas, who is seen as one of the most vulnerable Democrats up this cycle. Alison Lundergan Grimes, who Democrats hope can defeat Minority Leader Mitch McConnell in Kentucky, has also signed on to the campaign.
But it also has the support of Sens. Heidi Heitkamp of North Dakota and Robert Menendez of New Jersey.
Democrats bristle at the notion that, as some Republicans have argued, extending unemployment benefits is purely a political play.
"Fighting for American workers is part of who we are as a party, so it stands to reason that the issues on which Democrats campaign would reflect that," Coons spokesman Ian Koski said.