DAVENPORT, Iowa — Kristy Schneeberger, a Democrat in Eastern Iowa, said it was about time that Democrats in Congress moved to impeach President Trump. “No one is above the law,” she said.

But for Ms. Schneeberger and many other Democratic voters around the country, the prospect of an explosive impeachment battle in Washington also left them nervous. They worried that impeachment could easily backfire on Democrats, galvanizing Mr. Trump’s supporters in next year’s elections and drowning out people’s concerns about health care, immigration and the economy.

Gun control is a top priority for Ms. Schneeberger, 60, because her four adult children, ages 26 to 37, are teachers worried about their students’ safety. But now, she said, “I think it’s just getting sidelined again.”

While politicians in Washington crowded microphones on Wednesday to condemn or defend Mr. Trump and the prospect of his impeachment, more than two dozen voters across the country were by turns elated and wary, unsure and already exhausted, at the idea of an impeachment investigation that could consume the nation for months.