The Biden campaign is opening more field offices. Gov. Gavin Newsom has paid a visit, all the way from California, to proclaim the president’s fitness for a second term. And a recent poll has shown President Biden losing support.

New Hampshire’s famously independent-minded voters have reliably favored Democrats in presidential races for two decades.

But after Mr. Biden’s recent dismal debate performance, one poll of registered voters in the state found that former President Donald J. Trump had a slight lead. And the Cook Political Report, a nonpartisan election forecaster, changed its outlook this week for the presidential race in the state from “likely Democrat” to “lean Democrat.”

Those indicators, along with Mr. Newsom’s sudden appearance at highway rest stop near Manchester, raise a question that is infrequently asked in the state: Could New Hampshire, with its four electoral votes, be in play for Republicans?

In interviews this week, most voters said that they had already made up their minds — and that the debate, held last month in Atlanta, had not done much to sway them. For many Biden supporters, the prospect of another Trump presidency is enough to drive them to the polls.

Carol Knight, 86, from Nashua, an old mill city of 90,000, described herself as a loyal Biden supporter who would never budge because “democracy is at stake.”