Story highlights Democratic senators are starting to say whether they back a Bernie Sanders bill

The proposal concerns one of several plans described as 'medicare for all'

(CNN) Our weekly roundup of the news, notes and chatter about the prospects for the next Democratic presidential race:

Next week, Vermont Sen. Bernie Sanders will introduce his long-awaited single-payer health care bill with a cadre of the Democratic 2020 prospects expected to sign on as co-sponsors. Not long afterward, Connecticut Sen. Chris Murphy, another potential 2020 candidate, will propose an alternative: Allowing individuals and businesses to buy into Medicare.

Both ideas have, at times, been labeled "Medicare for all." But their differences also offer a glimpse at what's likely to be a defining debate within the Democratic Party in its next nominating contest: A full shift to a government health insurance system versus a partial step away from private markets.

It's possible for some Democrats to support both ideas. Murphy, in an interview with Politico , portrayed his bill as a more politically practical bridge to Sanders' goal. "We're not going to pass a single-payer health care bill any time in the next few years. And so we need to have a conversation about how we get there," he said.

Kamala Harris was the Elizabeth Warren The intra-party debate will heat up when Sanders' bill drops in the coming days. California Sen.was the first to announce she'd co-sponsor it. Massachusetts Sen. said Thursday in a fundraising email that she'd co-sponsor Sanders' bill, too. She wrote: "Medicare for All is one way that we can give every single person in the country access to high quality health care. Everyone is covered. Nobody goes broke paying a medical bill. Families don't have to bear the costs of heartbreaking medical disasters on their own."

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