Democratic presidential candidate Hillary Clinton, joined by Sens. Debbie Stabenow (D-Mich.), left, and Jeanne Shaheen (D-N.H.), center, speaks to voters Friday in Manchester, N.H. (Melina Mara/The Washington Post)

For the Democratic presidential candidates, there are two urgent campaigns underway in New Hampshire.

The first is over the size of what Hillary Clinton and Bernie Sanders agree is a likely Sanders victory here: Clinton is pulling out every stop to shrink what the latest polls show is a gap of 20 percentage points or more, while Sanders is striving for a win that would give his long-shot candidacy fresh momentum.

But the more consequential battle playing out on the ground here this week may be about what happens after New Hampshire — and which themes and issues will shape a potentially prolonged battle for the Democratic nomination.

At her appearances here this week, Clinton has tried to build a foundation to frame the choice before Democratic voters in the weeks ahead. “I’m a progressive who gets results,” she has said again and again.

It is not that Clinton is giving up on New Hampshire, a state where she in 2008 and her husband, Bill Clinton, in 1992 mounted comebacks. But however unlikely a victory in Tuesday’s primary may seem, Clinton is using the closing days of the New Hampshire campaign to set the tone for the contests in Nevada and South Carolina, as well as the dozens of big-state primaries and caucuses that follow in March and beyond.

Teacher and writer Andrea Ardito of Portsmouth, N.H., came to Exeter on Friday with her children to support Bernie Sanders in the final days before the primary there. (Dalton Bennett/The Washington Post)

Clinton plans to leave New Hampshire briefly on Sunday for a hastily arranged visit to Flint, Mich. She has regularly cited the lead-poisoned water crisis in the economically depressed and majority-African American city as an example of racial and economic inequality.

“Hillary is looking across a much broader and more diverse Democratic Party than the New Hampshire electorate,” said strategist Paul Begala, a Clinton loyalist. “An old professor of mine said there are parachutists and truffle hunters. Truffle hunters dig down real deep and focus on one thing, and parachutists look at the entire landscape. This is what’s going on here.”

The same could be said for Sanders. On Friday, the senator from Vermont accepted the endorsement of Benjamin Jealous, the former head of the NAACP. (Jealous was scheduled to join Sanders at a news conference at the historic town hall in Exeter, N.H., but a snowstorm snarled his travel plans, and the two men addressed reporters by phone.)

Sanders’s move was aimed at a much wider audience than predominantly white New Hampshire. It also comes as he is trying to boost his recognition and support among black voters, who account for more than half of the Democratic electorate in South Carolina, which holds its primary on Feb. 27.

But Sanders is hardly taking his eye off New Hampshire. Though his aides are trying to tamp down expectations, Sanders is doing everything he can to grind out a big win. His campaign is trying to frame the primary here as a test of general-election strength, considering the state’s large numbers of independent voters.

If he beats Clinton by a large margin, his advisers said, it would be a crucial springboard that gives immediate credibility to his insurgent bid.

“We want to build our vote as big as possible,” Sanders strategist Tad Devine said. “New Hampshire could be a huge momentum event. That’s what we’re shooting for.”

Children cheer as Democratic presidential candidate Hillary Clinton speaks with former congresswoman Gabrielle Giffords during a rally Tuesday in Hampton, N.H. (Jabin Botsford/The Washington Post)

Referencing Clinton’s hair’s-breadth win Monday night in the Iowa caucuses, Devine said, “The American voters didn’t understand until Iowa that he could beat her.” Part of the message his campaign is trying to convey in New Hampshire and beyond: “This guy is a national candidate who can take on Hillary Clinton.”

Sanders intends to use his victory speech here Tuesday night to lay out broader themes for the campaign going forward.

“It’s a precious opportunity to speak to the nation,” Devine said. He said it provides “a new audience that’s just beginning to be available to him. It means talking about some of this stuff in a little bit of a different language.”

Sanders will have another opportunity for national exposure this weekend when he heads to New York to appeal on NBC’s “Saturday Night Live,” aides said. Comedian Larry David, who has played Sanders with uncanny precision this season, is hosting this week’s show, and Sanders is expected to make a cameo.

Sanders faces several challenges when the race moves on from New Hampshire. The primary electorate in the first two states has been overwhelmingly white and liberal. Democratic voters in South Carolina and a slew of states voting in March are more diverse and centrist overall.

Sanders has benefited from spending large stretches of time in Iowa and New Hampshire, and voters over time have become better acquainted with the quirks of his politics, including his self-imposed label of democratic socialist. He is a more unfamiliar quantity in the other 48 states.

Clinton, by contrast, is universally known and has deep support among black and Latino voters nationwide. Her advisers argue that she is positioned well in later states to withstand whatever momentum Sanders has coming out of New Hampshire.

“They may give him a fresh look; I don’t think they’re going to move to him,” Joel Benenson, her chief strategist and pollster, said Friday at a Wall Street Journal breakfast. “I think she’s got a stronger argument about their struggles, their lives, their human experiences.”

Clinton has been arguing here that she is prepared for all aspects of the presidency — and implicitly, that Sanders is not — and would lead with her heart and her head.

“Hillary’s building a case that is much more likely to be durable over the course of the campaign than the one Senator Sanders is making,” said pollster Geoff Garin, who advises the pro-Clinton super PAC Priorities USA Action. “Realism starts to kick in as voters think more about the consequences of their decision.”

But some Democrats say her message is insufficient.

“It’s not clear to me that realism is a rallying cry,” veteran strategist Robert Shrum said.

“All those signs they hold up at her rallies, ‘Fighting for us’ — that needs to become a central, thematic womb for everything she’s saying,” Shrum added. “She needs to project a sense of vision. . . . She needs to put human clothes on the policy plans that she has.”

The Clinton team freely concedes the difficulty of defeating Sanders here. “We have a lot of work to do here,” campaign chairman John Podesta said.

But Clinton has vowed to slug it out in the Granite State.

“This state has been so good to my husband and me, and my family,” Clinton said Friday as she urged campaign staff and volunteers to brave heavy snow for a day of knocking on doors. “I am fighting for us, and I am not going to stop fighting for New Hampshire.”