The party’s voters are more evenly split on the scale of change they are seeking from their nominee: 49 percent said they preferred a candidate who would return politics in Washington to normal, while 45 percent hope for one who will bring fundamental change to American society.

The poll showed a top tier of three candidates in the battleground states: Former Vice President Joseph R. Biden Jr. and Senators Elizabeth Warren and Bernie Sanders. Mr. Biden was leading in five of the six states, while Ms. Warren enjoyed a narrow advantage within the margin of error in Wisconsin, where Mr. Sanders also appeared strong. No other candidate registered in double digits in any of the states surveyed.

While Democrats have unambiguously moved to the left in the decade since President Barack Obama took office, as Republicans eagerly point out, the poll illustrates that the party’s identity is more complex than the opposition and some progressive activists would portray it.

Democratic voters in the six states, each of which Mr. Trump carried three years ago, are split almost equally in how they described themselves ideologically: 49 percent say they are moderate or conservative, while 48 percent indicate they are very liberal or somewhat liberal.