It powered Democrats to recapture the House in the 2018 midterms: the fear that President Trump and Republicans would kill the Affordable Care Act and with it, protections for more than 50 million Americans with pre-existing medical conditions.

Yet even as Mr. Trump and other Republicans continue to try to overturn the law in court, Democratic presidential candidates have not made the issue central to their campaigns. Instead they have spent much of their time on the debate stage arguing among themselves over “Medicare for all” and other proposals to expand health coverage.

“I do think it’s a missed opportunity to educate voters about what’s really at stake in the fall,” said Leslie Dach, chairman of Protect Our Care, a group that ran a campaign-style war room in 2017 to defeat House Republicans seeking to repeal Obamacare, “and that’s having to stop Donald Trump’s relentless war on health care.”

Michael R. Bloomberg, the former New York City mayor who entered the Democratic presidential primary late and has not qualified to participate in the debates, has moved to exploit his rivals’ failure to mount a more frontal attack on Mr. Trump’s record on health care. Driven by extensive polling, Mr. Bloomberg’s campaign has released a torrent of television and digital ads accusing Mr. Trump of trying to “undermine coverage” for Americans with pre-existing conditions.