Presidential hopeful Elizabeth Warren, who called this week for the breakup of America’s biggest tech companies, was challenged on her capitalist credentials on Sunday. The exchange offered a preview of how Democratic presidential candidates might handle Donald Trump’s campaign strategy of stoking fears about “socialism” in attacks on his challengers.

Asked on CBS’s Face the Nation if she might properly be described as a capitalist, Warren, a former Republican who has done pioneering academic work in the area of consumer debt, said: “Yeah.”

“I believe in markets,” the Massachusetts Democrat said. “Markets that work. Markets that have a cop on the beat and have real rules and everybody follows them.”

Interviewer Ed O’Keefe followed up: “So if you get labeled as a socialist –”

“Well,” the senator replied, “it’s just wrong.”

It is unclear if the “socialist” charge will gain traction with voters in a negative way as the election approaches. In Gallup polling last year, 57% of Democrats said they held a positive view of socialism, compared with 47% who said the same for capitalism. It should also be noted that 6% of all poll respondents defined socialism as “being social”.

There is no doubt, however, that Trump intends to paint his opponents red.

“We are born free, and we will stay safe,” he said in his State of the Union address last month. “Tonight, we renew our resolve that America will never be a socialist country.”

Two weeks later, Trump told an audience in El Paso, Texas: “The Democrats have never been more outside of the mainstream. They’re becoming the party of socialism, late-term abortion, open borders and crime.”

Warren, who among the emerging Democratic field has unique experience in designing protections for consumers against predatory lenders, credit card companies and abusive banking practices, has drawn fire for years from Republicans concerned for the wellbeing of the financial industry.

As a candidate for president, the Massachusetts senator has proposed an “ultra-millionaire tax” on the country’s 75,000 richest families, universal childcare and “a new era of strong antitrust enforcement”.

Quick Guide Who are the leading Democrats running for 2020? Show Joe Biden, former vice president Biden unsuccessfully ran for the nomination in 1988 and 2008, and his campaign is likely to be dogged by controversy after allegations from several women they were left feeling uncomfortable by their physical interactions with him. If successful, Biden would become the oldest person to be elected president in US history. Mike Bloomberg, former New York mayor Bloomberg has expressed concern that none of the top candidates can defeat Trump, and he aims to make up for an unusually late entry in the Democratic primary with historic spending of hundreds of millions of dollars in television ad time and an unorthodox strategy of skipping the first four states in the primary. Bloomberg has announced that his campaign will be entirely self-funded, but can this billionaire win? Amy Klobuchar, Minnesota senator On Election Night 2018, Klobuchar coasted to a third term as senator in a state Trump almost won. Next morning she was on every short list of potential presidential candidates. Supporters say her success with rural voters makes her a formidable candidate in the Rust Belt, while her calm demeanour provides a clear contrast with Trump. Bernie Sanders, Vermont senator Sanders turned a long-shot, anti-establishment bid for the presidency into a “political revolution” that energized the party’s progressive base. His political career began nearly 40 years ago, but it wasn’t until his 2016 run that Sanders became a national figure as a new generation of Democrats – and 2020 contenders – embraced his populist economic policies. Elizabeth Warren, Massachusetts senator Her sharp criticism of Wall Street and big corporations has made Warren a favorite among progressive activists, and she will campaign on a message of a rigged economic system and income inequality.

Most of her proposals would fit comfortably in the campaign platforms of her fellow Democratic contenders. But her proposal to break up the tech giants Amazon, Facebook and Google has attracted a burst of attention – and attacks.

Asked about Warren’s plan on CNN’s Face the Nation, the Washington state governor, Jay Inslee, described a need “to protect Americans in this new economy” but declined to join Warren in her call for a tech breakup. Amazon is based in Seattle.

Warren’s call could have some bipartisan appeal. Writing in the Guardian on Sunday, the Clinton labor secretary Robert Reich said support for breaking up the tech giants was bipartisan. He quoted the Missouri Republican Josh Hawley, who told him: “Every day brings some creepy new revelation about these companies’ behaviors. Of course the public is going to want there to be action to defend their rights. It’s only natural.”

Warren speaks much more directly to the issue. Explaining her proposal at the South by Southwest (SXSW) festival in Austin, Texas, on Saturday, she drew a baseball analogy.

“You can be an umpire – a platform – or you can own teams,” she said. “But you can’t be an umpire and own one of the teams that’s in the game.”

On Sunday, Warren declined to turn her proposal into the argument over “isms” that Trump is spoiling for.

“I believe in a level playing field,” Warren told CBS. “And as long as we’ve got that then we will get the best out of markets because it means the people who come up with great ideas, who work hard, are the ones who will prosper, not simply those who were born into wealth.”

The rising Democratic star Alexandria Ocasio-Cortez also appeared at SXSW. Speaking on Saturday night, the New York congresswoman said that because “capitalism is an ideology of capital” and “the most important thing is the concentration of capital and to seek and maximize profit”, to her, “capitalism is irredeemable”.

The remark was duly seized upon on the right.