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(CNN) —  

A new NBC/Wall Street Journal poll out Tuesday finds former Vice President Joe Biden leads the field in the first national polling after last week’s Democratic presidential debate, but Sen. Elizabeth Warren of Massachusetts has risen to hold second place on her own.

The new polling comes after the debate brought to the fore a slew of new policy platforms for candidates to address, including gun policy and race relations, and continued the debate about the future of American health care.

The poll, fielded by phone from Sept. 13-16 and with a margin of error of plus or minus 4.36 percentage points for results among Democratic primary voters, showed Biden with 31% and Warren with 25%. The poll has Warren up 7 points since early July, the last time NBC and the Wall Street Journal released a poll, and is another survey showing Warren’s support has grown in recent months.

Sen. Bernie Sanders of Vermont was at 14%, South Bend, Indiana, Mayor Pete Buttigieg at 7% and Sen. Kamala Harris of California at 5%. Businessman Andrew Yang clocked in at 4%, Sen. Amy Klobuchar of Minnesota at 2% and Sen. Cory Booker of New Jersey at 2%. All the rest of the tested field landed at 1% or less.

Warren’s popularity came through in another facet of the poll: Thirty-five percent of Democratic primary voters say they would be enthusiastic about Warren, topping each of the other candidates tested on that measure by 10 points or more.

The poll also revealed some insight into voters’ policy preferences. Fifty-six percent say they prefer a candidate who “proposes larger scale policies that cost more and might be harder to pass into law, but could bring major change” over “smaller scale policies that cost less and might be easier to pass into law, but will bring less change.”

Respondents also shared their recollections of Barack Obama, who has been frequently referenced by Democrats looking to associate with – or distance themselves from – the former president.

Seventy-eight percent say they are satisfied that Obama’s presidency “did as much as was possible at the time in addressing the issues facing the country,” while 20% were “not satisfied because more should have been done to address issues facing the country.”