WASHINGTON—The White House’s top liaison to Capitol Hill will leave the job as early as this summer, lamenting to colleagues the “diminishing returns” of pushing President Donald Trump’s agenda through the Republican-controlled Congress as the midterm elections approach, according to people familiar with the conversations.

Legislative affairs director Marc Short told White House Chief of Staff John Kelly before the president’s trip to Singapore that he is likely to leave soon, according to the people. Asked to comment, Mr....