Words matter in politics and policy, and both Mr. Trump and Mr. Carson have made comments that make mayors and housing experts uneasy.

Mr. Carson once told a television interviewer that he had risen above his circumstances by realizing that “poverty is really more of a choice than anything else,” by which he apparently meant that people escape poverty through hard work.

That comment, spotlighted in a video mash-up on the Salon website, has dogged the neurosurgeon. So has an opinion piece he wrote in which he described fair housing policy as “social engineering.”

This plays into Mr. Trump’s sweeping declarations about black people living in “inner cities” rife with crime.

“I give Trump credit for talking explicitly about the importance of the inner city,” Ms. Liu said, “but we need to make sure that the policies really do address what is needed there. What we don’t need is just law-and-order tactics.”