By Eric Bradner

CNN

(CNN) -- Democrats eying the 2020 presidential contest could soon face a "Medicare-for-all" litmus test from the party's progressive base.

After last month's failure of President Donald Trump and congressional Republicans to repeal Obamacare, progressives are going on offense, mounting a new push for single-payer health insurance.

Leading the way is Vermont Sen. Bernie Sanders -- whose megaphone on the left is loud enough to force others vying to lead the party to weigh in, too.

At a Friday night Boston rally alongside another liberal firebrand -- Massachusetts Sen. Elizabeth Warren -- Sanders vowed to introduce a "Medicare-for-all" bill in Congress "within a month."

"If every major country on earth guarantees health care to all people and costs a fraction per capita of what we spend," Sanders said, "don't tell me that in the United States of America, we cannot do that."

Warren herself had already spoken and was off-stage by the time Sanders issued his call.

But a week earlier, she was asked at a town hall whether Democrats should pursue adding a "public option" for health insurance or single-payer health insurance. "Yes," she responded.

"My view on this is, when it's time to take a step back and say, 'What is the right way to do health care in America,' I think that's when it's time to put it all on the table. Not just small adjustments," she said.

Warren's hedge -- that Democrats need to wait for the right time -- showed that single-payer health insurance, or "Medicare-for-all" as Sanders puts it, is sure to become a gut check for all Democrats.

It's long been a policy dream of many liberals, but Democrats who live in states and districts that were carried in 2016 by Trump are certain to be sensitive to the political risks of supporting what Republicans call socialized medicine.

Still, progressive organizations began a major push last week.

The Progressive Change Campaign Committee, which calls itself the "Elizabeth Warren wing" of the party, circulated a petition starting March 28 seeking support for Sanders' proposal, stating that all Democrats on the ballot in 2018 "should publicly support and run on" passing the plan.

The failure of Trump and House Speaker Paul Ryan to shepherd the GOP plan through the House is one reason liberals are mounting a new Medicare-for-all push.

Another: President Barack Obama -- whose name is permanently attached to the Affordable Care Act -- has left the political stage. That means Democrats don't need to hold back their critiques.

In an email to supporters urging signatures for the group's petition, PCCC organizer Keith Rouda wrote that, "if we look with clear eyes, we have to admit that the ACA was a step forward, but it has significant shortcomings. Even with improvements to increase competition and lower costs, tens of millions of Americans will still be uninsured."

"We are already working with our friends in Congress to build momentum for this idea -- and make it a high-profile 2018 issue," Rouda wrote.