The U.S. Olympic Committee may drop Boston’s bid to host the 2024 Summer Games if local support doesn’t improve soon, people familiar with the organization’s plans said Tuesday.

USOC chief executive Scott Blackmun said his group will conduct independent polling in the next few months to monitor public sentiment. “Local support is critical to the success of any bid,” Mr. Blackmun said. Enthusiasm for the proposal has cratered among Boston-area residents, and people familiar with the USOC’s thinking said the group is unlikely...