A majority of voters support "Medicare for all" if they can keep their doctors, even if that means a diminished role for private insurance, a new poll finds.

The Morning Consult/Politico survey reports that 55 percent of voters support a Medicare for all system when told it would diminish the role of private insurers but that people could keep their doctors.

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When respondents are only told that Medicare for all would diminish the role of private insurers, the share supporting the idea falls to 46 percent.

The poll comes as Democratic presidential candidates are battling over how far to go towards a government-run, Medicare-for-all system, and whether to leave a significant role for private insurers.

Sens. Bernie Sanders Bernie SandersThe Hill's Campaign Report: Trump faces backlash after not committing to peaceful transition of power Bernie Sanders: 'This is an election between Donald Trump and democracy' The Hill's 12:30 Report: Trump stokes fears over November election outcome MORE (I-Vt.), Elizabeth Warren Elizabeth WarrenHillicon Valley: Subpoenas for Facebook, Google and Twitter on the cards | Wray rebuffs mail-in voting conspiracies | Reps. raise mass surveillance concerns On The Money: Anxious Democrats push for vote on COVID-19 aid | Pelosi, Mnuchin ready to restart talks | Weekly jobless claims increase | Senate treads close to shutdown deadline Democratic senators ask inspector general to investigate IRS use of location tracking service MORE (D-Mass.) and Kamala Harris Kamala HarrisHundreds of lawyers from nation's oldest African American sorority join effort to fight voter suppression Biden picks up endorsement from progressive climate group 350 Action 3 reasons why Biden is misreading the politics of court packing MORE (D-Calif.) are all supporting a system of government insurance for everyone, leaving only a very small role for supplemental private insurance.

Former Vice President Joe Biden Joe BidenPelosi slams Trump executive order on pre-existing conditions: It 'isn't worth the paper it's signed on' Hillicon Valley: Subpoenas for Facebook, Google and Twitter on the cards | Wray rebuffs mail-in voting conspiracies | Reps. raise mass surveillance concerns Fox News poll: Biden ahead of Trump in Nevada, Pennsylvania and Ohio MORE and South Bend, Ind., Mayor Pete Buttigieg Pete ButtigiegBillionaire who donated to Trump in 2016 donates to Biden The Hill's Morning Report - Sponsored by Facebook - GOP closes ranks to fill SCOTUS vacancy by November Buttigieg stands in as Pence for Harris's debate practice MORE, by contrast, are supporting giving people the option to get government-run insurance, while also letting private insurance remain for those who want it.

The poll finds that overall support for Medicare for all — when people are not told anything about private insurers or doctors — is 53 percent of voters.

That includes 77 percent of Democrats, 50 percent of Independents, and 27 percent of Republicans.