WASHINGTON—The polarized political climate is taking a toll on Sen. Susan Collins (R., Maine), who is facing a competitive race for the first time since she won a Senate seat in 1996, according to a new poll conducted after her closely watched votes in President Trump’s Senate impeachment trial.

Some 42% of respondents to a Colby College poll said that they would vote for Ms. Collins in November, compared with 43% who said they would vote for her expected Democratic rival, Sara Gideon, Maine’s House speaker. Ms. Collins won...