More than half of Democrats polled by The Washington Post and ABC did not provide a name when asked who they'd support in next year's presidential primary, suggesting a wide-open race for the right to take on President Trump Donald John TrumpUS reimposes UN sanctions on Iran amid increasing tensions Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Trump supporters chant 'Fill that seat' at North Carolina rally MORE.

Former Vice President Joe Biden Joe BidenMomentum growing among Republicans for Supreme Court vote before Election Day Trump expects to nominate woman to replace Ginsburg next week Video of Lindsey Graham arguing against nominating a Supreme Court justice in an election year goes viral MORE took 9 percent and Sen. Kamala Harris Kamala HarrisHarris honors Ginsburg, visits Supreme Court The Hill's Campaign Report: Trump and Biden vie for Minnesota | Early voting begins in four states | Blue state GOP governors back Susan Collins Kamala Harris: Black Americans have been 'disproportionately harmed' by Trump MORE (D-Calif.) won 8 percent support in the new poll released Tuesday.

But no other candidates cleared 5 percent support, and 56 percent of respondents did not name a candidate.

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Biden has yet to decide on whether to run in 2020, while Harris declared her campaign earlier this month.

Among other candidates who have declared, Sen. Elizabeth Warren Elizabeth WarrenBiden's fiscal program: What is the likely market impact? Warren, Schumer introduce plan for next president to cancel ,000 in student debt The Hill's 12:30 Report - Presented by Facebook - Don't expect a government check anytime soon MORE (D-Mass.) received 2 percent of support, while Sen. Kirsten Gillibrand Kirsten GillibrandSunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election Suburban moms are going to decide the 2020 election Jon Stewart urges Congress to help veterans exposed to burn pits MORE (D-N.Y.) and former San Antonio Mayor Julián Castro received less than 1 percent.

The poll did suggest Trump is vulnerable.

Fifty-six percent of all Americans surveyed would “definitely not vote for" Trump if he is the Republican nominee, including 59 percent of independents and 64 percent of women.

Fourteen percent of all respondents said they would consider voting for Trump, and 28 percent said they definitely would.

Nearly 1 in 3 Republican respondents said they would like to nominate someone other than Trump.

The Post-ABC poll surveyed 1,001 adults between Jan. 21 and 24. The margin of error for the sample is 5.5 percentage points.