But their national parties are another story.
Jones' campaign has worked hard to convince Democrats to take seriously the former prosecutor's chances of defeating Moore -- the twice-removed former Alabama Supreme Court chief justice whose theocratic campaign message has alienated some moderate and pro-business Republicans.
"Doug knows Alabama. He knows your heart, and he'll never let you down," Biden said Tuesday in Birmingham, echoing Jones' argument that Moore would be likely to embarrass the state.
The tactics are similar to those that carried Democrat John Bel Edwards past Republican Sen. David Vitter, who had been ensnared in a prostitution scandal, in the Louisiana governor's race in 2015.
But one big question for national Democrats is whether donors' desire to keep Moore out of the Senate will translate into huge and sustained fundraising figures that Jones would likely need.
Some donors could shy away from the Alabama race after being burned by this summer's special elections in deep-red House districts -- including the $30 million pumped into Jon Ossoff's unsuccessful campaign in Georgia
The Senate Majority PAC, the major Democratic super PAC focused on Senate races, and the Democratic Senatorial Campaign Committee are still watching to see how the race develops before deciding whether to get involved -- keenly aware that Jones being seen as a candidate backed by the Democratic machine would be fatal in deep-red Alabama.
But Jones has attracted some support from Democrats and progressive activists who are eager to see the party put up a fight in the South, particularly against Moore, whose public persona is built in part on his opposition to LGBT rights.
Jones was shepherded around Washington during a recent Congressional Black Caucus conference by Alabama's lone Democratic congresswoman, Terri Sewell, and consultant Joe Trippi. At a private lunch, Sens. Tim Kaine of Virginia and Chris Van Hollen of Maryland urged fellow Democrats to back Jones.
His trip included meetings with progressive groups such as DailyKos.com -- the blog that injected rocket fuel into Ossoff's online fundraising efforts, but has not yet endorsed in the Alabama race.
Jones met with Democracy For America electoral director Annie Weinberg, and the group used its fundraising list to boost Jones this week.
"Doug Jones took on the KKK and won. Roy Moore is a radical extremist who was kicked off the Alabama Supreme Court twice for his hateful views. We have to stop Roy Moore -- and support Doug Jones," DFA senior campaign manager Robert Cruickshank said in a fundraising email.
Another left-wing group, the Progressive Change Campaign Committee, is railing against Moore -- but is taking the more cautious approach of urging donors to split their contributions among Jones, Wisconsin Sen. Tammy Baldwin and Massachusetts Sen. Elizabeth Warren, two pro-LGBT bulwarks.
The Democratic National Committee has also sent fundraising emails on Jones' behalf, highlighting his career as a prosecutor who put two former Klansmen involved in the 1963 16th Street Baptist Church bombing behind bars.
Jones also impressed Democrats -- and some Republicans -- with his first post-Republican primary interview with NBC's Chuck Todd.
But one progressive strategist said Jones is unlikely to come anywhere close to generating the donor interest that Ossoff received because his profile as a moderate Democrat won't excite progressive donors across the country who are looking for anti-Trump firebrands.
It's not just Democrats who are tepid about the Alabama Senate race.
The Bannon-aligned Great America PAC is asking if Mitch McConnell's super PAC, the Senate Leadership Fund, which spent more than $10 million backing Strange in the primary, is "unwilling to spend as much to defeat a Democrat as they were willing to waste smearing a fellow Republican."
"The best way for Mitch McConnell to atone for this mistake is for him and his allies at the Senate Leadership Fund to put their money where their mouth is and provide Judge Moore with the same level of financial support in the general election as they gave to Strange in last week's Republican runoff," Great America PAC strategist Ed Rollins said in a statement.
The Senate Leadership Fund declined to comment on the email blast. The super PAC said after Moore's primary victory that it would support him, but has not spent in the race yet, with the December 12 general election is still more than two months away.
Moore was in Washington on Wednesday for meetings -- including a visit with Steve Bannon, the former White House chief strategist who has provided Washington muscle for anti-establishment Senate primaries, and a huddle in the Capitol Hill Club with the state's Republican congressional delegation. Bannon and Moore met for two hours.
Rep. Mo Brooks, the third-place finisher in Alabama's Republican primary behind Moore and Sen. Luther Strange, said afterward he was "not going to discuss any of our strategies on helping make sure that Doug Jones, liberal Democrat, does not win."
But as of lunch time, the state's senior senator, Richard Shelby, still hadn't heard from Moore. The two hadn't spoken, he said, since Moore won the September 26 primary runoff against Sen. Luther Strange for the seat formerly held by Attorney General Jeff Sessions.
"If he calls me, I'd be glad to meet with him," Shelby said.
"I'm a Republican. I'm going to support the ticket. Roy Moore is the nominee," Shelby said. "I think there will be other people on the ticket too. Local races. I don't know. I support them all."