In the special-election race that wrapped up last week, Mr. Booker campaigned on working across the aisle despite the bitter partisan divide in Washington. Drug policy could be one area where he finds some success, according to those who work in the field. He singled out Sen. Rand Paul of Kentucky, a libertarian, as someone who sees eye-to-eye with him on the issue.

"I want to work with him," said Mr. Booker, about Mr. Paul, during an interview Tuesday at his campaign office in the city he led as mayor for seven years. "I take everybody in the Senate as sincere people who want to make a difference."