The docket of the Supreme Court this year is packed with core liberal issues: abortion access, federal protection for LGBT workers and gun rights. But given the court's 5-4 conservative majority, liberals are nervous about how those cases will be decided — and how future issues will be resolved if the balance shifts further after 2021. At the same time, they're also viewing this as a prime opportunity to press Joe Biden to make his case for the White House by running on the judiciary.

In doing so, Biden might galvanize his moderate base and bring along reluctant progressives. It's the same approach used by conservative groups for decades.

"We are about 40 or 50 years behind the conservatives on realizing that a lot of excitement actually happens at the courts," Indivisible Project's director of democracy policy Meagan Hatcher-Mays told CBS News. She cited the Supreme Court's recent decision regarding Wisconsin's primary, which effectively forced voters to brave the polls during the COVID-19 pandemic, as a clear example of how the high court's decisions can directly impact lives.

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Several lawyers and activists told CBS News that Biden, a former public defender, should run on protecting the popular liberal legacy of Ruth Bader Ginsburg.

Progressives warn if Biden is not elected, the Supreme Court's current 5-4 conservative tilt could balloon into a potential 7-2 majority if Ginsburg, 87, and Stephen Breyer, 81, choose to retire or face greater health troubles.

This outlook is too grim for voters like twins Tonya and Tiffany Hamilton, 37, who, while waiting in line at Biden's St. Louis rally in March, talked about Ginsburg's cancer treatment. Tiffany Hamilton pleaded, "All we need is her to hold on until at least November!"

Ginsburg is an enormously popular figure in the Democratic Party, a truth that has been evident throughout the Democratic primary process — her portrait is frequently seen beaming on colorful t-shirts and tote bags. Some suggest that by tying his campaign to protecting her legacy, Biden would also highlight his previous pledge to nominate the first black woman justice if he is elected.

There are now calls for Biden to copy the playbook of then-candidate Donald Trump, who in May 2016 released a list of 11 people he would pick from to nominate to take the late Justice Antonin Scalia's seat.

Hillary Clinton, the eventual Democratic nominee, did not release a list, since President Barack Obama had already nominated Merrick Garland, whose confirmation the Republican-controlled Senate blocked.

Demand Justice, a progressive court reform group, already has a list of several women who they view as qualified, including NAACP Legal Defense Fund Director Sherrilyn Ifill and California Supreme Court Justice Leondra Kruger.

Other names floated to CBS News as potential court picks for Biden included federal court judges Kentanji Brown Jackson and Tanya Chutkan, both Obama appointees to the federal bench.

"Clinton and [Tim] Kaine really needed a third person on that ticket to really get out individuals who weren't that excited by them as a team, and I think Joe Biden kind of has the same issue going forward," Melissa Murray, law professor at New York University and host of the Supreme Court-focused podcast "Strict Scrutiny," told CBS News. "Imagine how much more energizing it would be to also pick someone [for SCOTUS] who would excite parts of the Democratic base."

Polling supports the strategy. Almost two-thirds of Democrats said the court was too conservative, leaving the left's approval rating for the Supreme Court at 38% according to Gallup, the lowest it has been since the end of the Bush administration.

Asked about the likelihood of releasing a list of potential appointees, Biden's campaign did not directly respond and highlighted his history with the Supreme Court.

"As chair of the Senate Judiciary Committee, Joe Biden was proud to oversee and support the confirmation of Justices Ginsburg and Breyer and lead the fight against many Reagan judicial nominees with horrible records on civil rights and civil liberties, like Judge [Robert] Bork. As Vice President, he advised President Obama on the selection of Justices Sonia Sotomayor and Elena Kagan, and played a major role in winning their confirmation; Kagan previously served on Biden's staff," National Press Secretary TJ Ducklo said in a statement, "As president, Biden would appoint judges who share his values and would protect the Constitution, and has promised to make history by appointing the first African-American woman to the Supreme Court of the United States."

More broadly, there are also calls for Biden to outline how he plans to navigate his policy proposals through both a Senate that is unlikely to have a filibuster-proof Democratic majority and a conservative court that could challenge legislation.

"Biden is going to need to have a strategy to deal with the courts in order to get anything done on his agenda," Demand Justice executive director Brian Fallon told CBS News.

Any Biden administration wins on issues like gun safety, climate change or voting rights are "going to run head-long into a hostile court based on the 200-plus judges that Donald Trump has confirmed," Fallon explained.

The specter of conservative resistance is already on the Biden campaign's radar. In a recent letter addressed to the Trump administration and Republican governors, the campaign argued that they should drop their lawsuit against the Affordable Care Act.

"We are all fighting, we are all putting as much energy as possible to getting these progressive reforms passed just to watch the Supreme Court strike them all down," Indivisible's Hatcher-Mays added. "It's not worth the grassroots energy if we know that's going to be the outcome."

But while Biden seems to be ready to fight over Obamacare, on the trail he has shied away from other progressive ideas to remake the courts and Congress.

Elizabeth Warren in her presidential campaign called for the elimination of the Senate's 60-vote filibuster rule, which would lower the bar to pass legislation to a simple majority of 51 votes. And Pete Buttigieg detailed a whole plan to shake up the Supreme Court by adding more justices in an effort to "depoliticize" the court.

Asked about court reforms like these during his New York Times editorial board interview in January, Biden said he did not support any of them.

"The fact that you're going to amend the Constitution on judicial independence is kind of a stretch," he said.