Democratic presidential nominee Hillary Clinton spoke at the Congressional Hispanic Caucus' awards gala where she took aim at rival Donald Trump, saying that Trump spews "bigotry and hate." (Victoria Walker/Photo: Melina Mara/The Washington Post)

Tiny New Hampshire has just four votes in the electoral college, but Tim Kaine was back here for his third visit in five weeks. At back-to-back campaign appearances, Hillary Clinton’s running mate offered a blunt reason for why.

“This race is close,” the senator from Virginia said at a rally Thursday in this picturesque New England town. “I would rather be us right now than them. I think we have a more straightforward path to win and they have a more complicated path. But [there is] nothing to take for granted because, let’s be honest, it’s been a season of surprises.”

To many Democrats, the biggest surprise is that Donald Trump has mounted a comeback. Despite being battered all summer by his own missteps as well as a barrage of attack ads from Clinton, the Republican nominee has been surging in the battleground states.

Public polls over the past week show Trump leading Clinton in Ohio, Florida and Iowa; moving into a virtual tie with her in Nevada and North Carolina; and cutting into what had been comfortable Clinton leads in New Hampshire as well as in Colorado, Michigan, Pennsylvania and Virginia.

Clinton’s return to the campaign trail after her highly publicized bout with pneumonia came at what has turned out to be the low point for her of the general election. She is laboring to regain solid footing before the first of three debates, on Sept. 26.

Clinton said she believes Trump has helped her in recent days by reopening painful wounds with a discussion of his long-held “birther” conspiracy. After five years of peddling lies and innuendo about the circumstances of President Obama’s birth, Trump on Friday bowed to the facts and acknowledged for the first time that Obama was born in the United States, although he refused to apologize for his efforts to delegitimize the nation’s first black president.

It is too early to know whether the episode will be a turning point that reverses gains for him in many of the battleground states. Clinton has fundamental advantages in an electoral map that is tilted generally in favor of Democrats because of changing demographics, giving her more mathematical permutations than Trump to win.

State by state, Clinton’s advisers have a sober assessment of where the race stands. But they say that if they can turn out their votes — especially among young people, a critical Democratic constituency that has registered soft support for Clinton — they have ample ways to block Trump from winning the necessary 270 electoral votes despite clear deterioration in several states.

“We expected this to tighten. We expect it to tighten even further,” Clinton campaign manager Robby Mook said. “That’s why we built a robust campaign in all 50 states, but especially in the battleground states. It’s going to come down to small margins. . . . We’re spending a lot of time making sure of our vote.”

For the first time since Trump secured his party’s nomination in May, there is genuine confidence among Republicans that he could win. Trump campaign manager Kellyanne Conway said, “We own both the momentum and enthusiasm dynamics right now.”

“Everybody loves a winner, so people now see these polls tightening where we’re up, tied or within the margin of error in nearly all of the swing states,” Conway said. “People are starting to see that Trump can actually pull this off.”

Strategists for Clinton and her top allied super PAC, Priorities USA, are intently analyzing the polling shift to understand the forces propelling Trump.

Nowhere have Trump’s gains been more consistent than in Ohio, a swing state that Obama carried twice and where the Clinton campaign has been vastly outworking Trump’s on the ground and outspending it on the airwaves. In the RealClearPolitics average of recent Ohio polls, Trump leads Clinton 42.5 percent to 40.8 percent in matchups that include both third-party nominees, Gary Johnson of the Libertarian Party and Jill Stein of the Green Party.

Geoff Garin, the Priorities USA pollster, said Trump’s surge in Ohio and elsewhere is largely due to his consolidation of Republican and Republican-leaning independent voters. He said that at the moment, at least, these voters — the Mitt Romney coalition in 2012 — see Trump as an acceptable alternative to Clinton following several weeks of relatively disciplined campaigning by Trump.

“The phenomenon we are seeing right now primarily is just Donald Trump being normalized among Republican voters,” Garin said. But, he cautioned, it “doesn’t get him beyond the 2012 map in any form or fashion.”

Stuart Stevens, who was Romney’s chief strategist and is not backing Trump, agreed: “I don’t think the structure of the race has changed. The structure favors any Democrat, and it particularly favors Clinton over Trump because Trump doesn’t have a campaign.”

At Clinton’s New York headquarters, her aides attribute much of the movement to which candidate is under fire and which one is out of the headlines. They have seen erosion in her support among white voters during difficult weeks, although they argue that those voters have shifted to the undecided column rather than moving all the way to supporting Trump.

The Clinton campaign is pessimistic about both Ohio and Iowa, which Obama also won twice. Public polls show Trump ahead in both — and comfortably so in Iowa, an overwhelmingly white state and one of the only battleground states in which the Republican establishment has fully embraced Trump. A Monmouth University survey this week showed Trump ahead of Clinton there, 45 percent to 37 percent, with Johnson running in third, at 8 percent.

Florida, another state Obama twice carried, remains extremely competitive, according to public and private polls, and probably will be until the end. Clinton advisers, however, note that they can lose all three of those states and still win the presidency.

Their position is strengthened, they argue, by what they say are strong standings in Virginia and Colorado because of the demographics there, though some public polls show a tightening race in the latter.

Clinton advisers are zeroing in on North Carolina as a potential back-breaker for Trump. In 2012, it was the only major swing state that Romney won, but it is by no means a sure thing for Trump. The RealClearPolitics average of polls there has Clinton hanging to a razor-tight lead, 42.8 percent to Trump’s 42.2 percent, with Johnson at 7.2 percent.

Joel Benenson, Clinton’s chief strategist and pollster, called North Carolina a “roadblock” state. “If we win North Carolina, along with Virginia, where we are in very good shape, we choke off so many paths to 270 that he’s threading a needle that has a smaller eye than any previous Republican candidate.”

Trump has demonstrated growing support across much of the Midwest, and Clinton’s team is closely watching Pennsylvania and Michigan, two states Republicans haven’t won in six straight elections. Clinton’s campaign has invested heavily in its ground organization in both states. A campaign official said that if Michigan became truly competitive, “that would create complications” in their electoral college calculations.

New Hampshire’s four electoral votes and Nevada’s six votes might seem trivial at first glance, but both campaigns recognize that if the election ends up in a photo finish, either or both of those states could play decisive roles.

Hours after Kaine’s appearances here Thursday, Trump punctuated the attention New Hampshire is getting with an evening rally at the middle school in Laconia.

An overall worry for Clinton is the apparent lack of enthusiasm among millennials; polls show her underperforming compared with Obama’s results among younger voters. Clinton advisers say that young people are “allergic to Trump,” as one put it, but not fully sold on Clinton. The campaign’s fear is that young voters either stay home in November or decide to cast ballots for one of the third-party candidates. “We need to get them feeling better about her,” one official said.

Benenson said of voters ages 18 to 34, “We are going to continue to galvanize them, organize them and get them out to the polls in November.”

To that end, Kaine visited a hip art cafe Thursday in Portsmouth, N.H., where he spotlighted issues for young professionals. He seized on Trump’s new child-care policy requiring six weeks of paid maternity leave for mothers, but no benefits for fathers, as a way of stamping Trump as a candidate from “an older era” whose idea does not take into account today’s generation of families.

Two liberal Clinton supporters popular with millennials — Sens. Bernie Sanders (Vt.) and Elizabeth Warren (Mass.) — are fanning out to college campuses across Ohio this weekend on Clinton’s behalf.

Coming out of the two July conventions, Clinton registered solid and in some cases double-digit leads nationally and in the swing states. The conventional wisdom focused not on whether Clinton would beat Trump but on how big her landslide might be.

Clinton’s aides said one of their biggest concerns then was complacency — that her supporters, believing Clinton’s win to be in the bag, would do little to volunteer in the fall or, worse, stay home on Election Day. For a campaign without much to celebrate in the polls, the new atmosphere at least is a welcome antidote.

“I’m not a big landslide guy,” Kaine told the Exeter crowd. “Hillary’s attitude is, ‘I’m an underdog — until I’m the winner.’ ”