After two weeks of dueling conventions witnessed by tens of millions of Americans, the contest between Hillary Clinton and Donald Trump has settled into a tight race — and intensifying heat — within 100 days of Election Day.

In the enduring, and conflicting, messages of the two nominees’ acceptance speeches lie keys to their chances of appealing to voters still skeptical, or even hostile — particularly undecided independent voters, and especially moderate suburban women — in the remaining three months of the campaign.

“These moderate women… if Hillary Clinton can push the vote of white women up substantially enough, she wins this election,’’ says Kathleen Hall Jamieson, director of the Annenberg School of Public Policy at the University of Pennsylvania. Clinton’s “convention structure was working with white women — if enough of them can be pushed, that wins the election.”

As is customary in modern, back-to-back conventions, the polling “bounces” for each nominee have essentially cancelled each other out.

A CBS News post-convention national survey found a bump for the Democrat: Clinton 46 percent, Trump 39. CBS had found the two tied following Trump’s convention. Clinton expanded her lead among women in the newest survey.

Another post-convention survey of 11 battleground states by CBS News found “a slight bump” for Clinton in the states that will determine the election: Leading Trump by just 43-41 percent. Trump was leading by only 42-41 coming out of his convention. Her gains in critical states such as Florida, Ohio and Virginia were recorded among Democrats and others undecided before her convention.

In a Morning Consult survey after the last convention, Clinton led Trump by 43-40 percent, compared with Trump’s four-point edge following his convention. A Reuters-Ipsos survey during and a day after her convention gave her five points.

In a daily tracking survey by the Los Angeles Times and University of Southern California, Trump’s apparent advantage over Clinton peaked at seven points after his convention and had slipped to four points by Sunday.

Heading into Trump’s convention, a CNN/ORC poll found Clinton ahead by seven percent: Clinton 49, Trump 42. After his convention, Trump led by three: 48-45.

FiveThirtyEight’s Nate Silver, who as recently as early July had rated Trump’s chances of winning the presidency at 20 percent, now placed the odds at virtually 50-50 for each — Clinton 51, Trump 49 — based on a state-by-state analysis.

The conventions were barely finished when Trump prompted controversy anew in a broadcast war of words with the American Muslim parents of a U.S. Army captain killed in action in Afghanistan, Khizr and Ghazala Khan. After reports of Trump’s criticism of the mourning parents’ stage appearance at the Democratic convention, they offered news outlets blistering rebukes of Trump’s “fear-mongering” and lack of respect for their son’s sacrifice.

“I think I have made a lot of sacrifices,” Trump said on ABC News’ “This Week.” “I’ve worked very, very hard. I’ve created thousands and thousands of jobs.”

If someone can’t empathize with a “Gold Star” family, Clinton running mate Tim Kaine said while campaigning, ”there is something fundamentally missing in your personality.” Clinton’s take: Trump “poses a serious threat to our democracy.”

Yet Clinton, appearing in a post-convention interview with “Fox News Sunday,” was asked why the contest remains so close.

“Too many Americans feel that they’ve been left behind, by our economy, by our government… They are looking for answers,” she said. “The kind of inflammatory arguments that Trump has provided… are attractive in the first instance (but) he has offered nothing to help people.”

Trump finds his strongest support among white men — particularly older men, and men with high school or less education. His convention calls for “law and order” and adamant defense of the right to bear arms play well to men. Clinton draws her greatest support from the college-educated, women and minority voters. Her convention conveyed a message of family values appealing to maternal instincts.

In their potential appeals to undecided women, both Clinton and Trump are drawing upon the family stories of daughters who introduced them to national television audiences and are likely to become crucial campaign trail surrogates in the months ahead: Chelsea Clinton, and Ivanka Trump.

“The Trump children, two of them tell you their fond memory of their father is sitting on the floor of his office playing with blocks of the things he was building,” Jamieson says. “They don’t have too many memories of him taking him to soccer or telling bedtime stories… What Chelsea said is that, yes her mother was away, but even when she was away she was there, ‘she left me little notes.’”

Slightly more people viewed Trump’s acceptance speech on television, 35 million, than those who watched Clinton’s, 34 million, according to Nielsen.

Among the central messages of their acceptance speeches, these refrains are likely to be repeated throughout the remaining campaign:

— Trump: This is “a moment of crisis for our nation. The attacks on our police, and the terrorism in our cities, threaten our very way of life… America is far less safe and the world is far less stable than when Obama… put Hillary Clinton in charge of America’s foreign policy.”

— Clinton: “America is once again at a moment of reckoning.” Trump “wants to divide us — from the rest of the world, and from each other… He’s taken the Republican Party a long way — from ‘Morning in America’ to ‘Midnight in America.’”

— Trump: Clinton has “bad instincts… bad judgment… This is the legacy of Hillary Clinton: Death, destruction and terrorism and weakness.”

— Clinton: “Donald Trump can’t even handle the rough-and-tumble of a presidential campaign. He loses his cool at the slightest provocation… A man you can bait with a tweet is not a man we can trust with nuclear weapons.”

— Trump: “Nobody knows the system better than me, which is why I alone can fix it… I will restore law and order to our country.”

— Clinton: “Don’t let anyone tell you we don’t have what it takes. We do.
And most of all, don’t believe anyone who says: ‘I alone can fix it.’”

— Trump: “We must immediately suspend immigration from any nation that has been compromised by terrorism… We don’t want them in our country… We are going to build a great border wall to stop illegal immigration.”

— Clinton: “We’ll build a path to citizenship for millions of immigrants who are already contributing to our economy. We will not ban a religion… Comprehensive immigration reform will grow our economy and keep families together.”

— Trump: “My opponent wants to essentially abolish the 2nd Amendment…” I “will protect the right of all Americans to keep their families safe.’”

— Clinton: “I’m not here to take away your guns. I just don’t want you to be shot by someone who shouldn’t have a gun in the first place.”

— Trump: “We will make America strong again. We will make America proud again. We will make America safe again. And we will make America great again.”

— Clinton: “What part of ‘America First’ leads him to make Trump ties in China… Trump suits in Mexico… He could start by actually making things in America again.”

In a contest of two nominees sharing dauntingly negative images in the minds of most of the voting public, both Trump and Clinton are accentuating the negatives about each other in pursuit of the same unconvinced Americans.

“So much of the swing vote falls into that category (of moderate women) — they know that children go through phases before they learn impulse control,” Jamieson says. The Clinton “campaign is working aggressively to say, ‘You ought be afraid of him and you don’t have to be afraid of her… You don’t have to like everything about her, but she’s the better choice.’”

“Hillary, that’s all they talk about is temperament,’’ Trump said on “This Week,” calling his rival “a very dishonest person. …I have a winning temperament. She has a bad temperament… I beat 16 very talented people (in the primaries), and I’ve never done this before. You don’t do that with a bad temperament.”