Hillary Clinton is maintaining her edge over Republican rival Donald Trump despite recent campaign setbacks, but the 2016 presidential race continues to tighten going into the homestretch, a new Wall Street Journal/NBC News poll has found.

After a rocky week of controversy over her health and for calling some of Mr. Trump’s supporters “deplorables,” the Democratic nominee leads Mr. Trump by 6 percentage points, 43% to 37%, among people likely to vote, the survey found. Two third-party candidates drew 12% support.

It...