The contrast was even more dramatic for Senator Kirsten Gillibrand, who captured every county along the Hudson River and beyond, all the way to the Canadian border — except for Putnam.

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The county seems like a curious outlier, a land that Democrats forgot along the Metro-North line, a place that, at its southernmost point, is roughly 50 miles to the New York City border and yet a world away.

Republicans, who outnumber registered Democrats in Putnam by about 3,000 people, have dominated politics there for decades; the only Democratic presidential candidate to win Putnam County in the last century was Lyndon B. Johnson.

Ms. Fleming, who unsuccessfully ran as a Democrat for county executive this year, and Ms. Croft, the county’s Democratic elections commissioner, know what they are up against. But you don’t have to be a politician to understand how the political dynamics can shape their lives.

“As a general rule, I do avoid talking about politics because the majority of the people that live here are highly conservative, and their viewpoints are very different from mine,” said Paula Bryan, a county resident who said she had been harassed in Facebook groups.