Looking at the full pool of potential persuadables, it can be hard to glean any clear insights. But individual demographic groups present a clearer picture of voters pulled in different directions by their ideology, identity, self-interest or attitudes about the president.

The white college-educated persuadable voters, in either the broad or narrow definition, have something in common: They may not love the president, but they are not sold on progressives.

They oppose single-payer health care, 60 percent to 37 percent, and oppose free college, 55 to 41.

They disapprove of the president, but only 32 percent disapprove of both his performance and his policies.

Steven Basart, 28, is getting his Ph.D in computer science and describes himself as a Democrat. Yet he would consider voting for Mr. Trump, depending on the Democratic nominee.

If it were Ms. Warren, he’d vote Republican, he said: “I think she’s going too far to the left, which would take our country in a bad direction.”

Mr. Basart is not a fan of Mr. Trump’s personality, but he says it’s overshadowing some of his accomplishments.

“There are plenty of things not to like about Trump, because he says things that are not nice and potentially racist,” said Mr. Basart, who is Latino. “I care somewhat about those things, but I mostly just care about policies, because at the end of the day, that’s what affects people.”