“What’s not to like? She’s pro-Israel, she’s a strong leader, she’d be the first woman president,” said Tobey Harman, a retired teacher. “The email thing, it’s a Washington and New York thing, meaningless to regular people.”

The controversy dogging Mrs. Clinton — that she used a personal account for government business, and chose what emails to delete or turn over to the State Department — is too recent to show up in the latest New Hampshire polls. Those show Mrs. Clinton as a runaway front-runner in the New Hampshire Democratic primary; she also leads Jeb Bush and Rand Paul by roughly 10 percentage points each in hypothetical general-election matchups in the most recent WMUR Granite State Poll.

But analysts and pollsters said the imbroglio could grow into a problem with voters, including some women, if Mrs. Clinton comes to be seen as unduly secretive or imperious in the months ahead.

“The Clintons have drawn sympathy and loyalty from New Hampshire voters in the past, but I don’t think women, or men, will look sympathetically on her if they see her as having a problem with secrecy and management,” said Andrew Smith, a political scientist and director of the Survey Center at the University of New Hampshire. “This is a legal process issue, not a personality attack on her that you can easily finesse.”

But Democrats and others here have a way of rallying to the Clintons in times of crisis. At a low point in Bill Clinton’s 1992 run, voters responded enthusiastically to an appeal he made in Dover just before the primary: “I’ll never forget who gave me a second chance and I’ll be there for you until the last dog dies.” And in January 2008, Mrs. Clinton came to Cafe Espresso to face a group of undecided voters on a day when her own campaign’s polls predicted that she would lose the primary. After one woman asked how she was holding up, Mrs. Clinton began to reply in a low, halting voice, far different from the confident energy that typically infused her public remarks.