A significant majority of Americans would favor a wealth tax on the nation's 75,000 richest families to pay for a new higher education initiative put forward by Sen. Elizabeth Warren Elizabeth WarrenDimon: Wealth tax 'almost impossible to do' CNN's Don Lemon: 'Blow up the entire system' remark taken out of context Democrats shoot down talk of expanding Supreme Court MORE (D-Mass.) that would make state and community colleges tuition-free and pay off most existing student loan debts, according to poll released Monday.

In the latest Hill-HarrisX survey, 64 percent of registered voters said that they would support such a plan.

(The poll did not attach Warren's name to the proposal, and instead summarized its provisions.)

The Massachusetts senator has been making new policy provisions the cornerstone of her campaign to become the Democratic Party's 2020 presidential nominee.

Warren has so far lagged behind former Vice President Joe Biden Joe BidenBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Democratic groups using Bloomberg money to launch M in Spanish language ads in Florida Harris faces pivotal moment with Supreme Court battle MORE and fellow Sen. Bernie Sanders Bernie SandersOutrage erupts over Breonna Taylor grand jury ruling Dimon: Wealth tax 'almost impossible to do' Grand jury charges no officers in Breonna Taylor death MORE (I-Vt.) in polls, while earning attention for a series of detailed policy goals.

Her college affordability initiative was supported by 67 percent of women contacted for the survey and by 60 percent of male respondents. It also attracted a large majority of support from all racial groups.

The proposal was also supported across all age groupings although voters who are 65 years old and up were somewhat less likely to support it. Sixty-seven percent of respondents between 18 and 64 said they backed Warren's idea compared to 53 percent of voters who were older.

Fifty-eight percent of respondents living in households making $75,000 or more a year said they supported the education and tax proposal. Respondents who made less than $75,000 were even more enthusiastic, backing the new policy by a 69-31 percent margin.

Voters who identified as Republicans or conservative of some stripe were the only demographic groups that opposed Warren's proposal, the survey found. Even so, Republican respondents were fairly evenly split with 52 percent saying they opposed the policy initiative and 48 percent saying they supported it. The division is well within the 5 percent sampling margin of error for that group. The overall survey has a 3.1 percent sampling margin of error.

Respondents who identified as Democrats backed the idea overwhelmingly, 78-22 percent. Independents favored the proposal by a significant 66-34 percent majority.

The strong support from Democratic respondents indicates that Warren's idea could be good for her politically, Lee Miringoff, a pollster who directs the Marist Institute for Public Opinion, said Monday on "What America's Thinking."

"People want people to go to college, people think people need to go to college, people know college is not particularly affordable," Miringoff told host Jamal Simmons.

"I think, especially on the Democratic primary field, it makes for really good politics," he said.

While most Americans currently seem to support Warren's proposal, the numbers could potentially shift over time once its details become more known and subject to challenge from political opponents, Carl Cannon, the Washington bureau chief at RealClearPolitics said Monday on "What America's Thinking."

"If this policy ever became taken seriously ... other questions would start to arise. Colleges that have quadrupled and quintupled their administrators, is that really necessary?" Cannon told Simmons, citing potential cost and fairness concerns that critics might raise.

—Matthew Sheffield