WASHINGTON — Hillary Clinton on Tuesday tried to build on her successes in the first presidential face-off, calling Donald Trump "dangerously incoherent" as she campaigned in North Carolina. Trump, meanwhile, blamed the sound system at the debate hall for his repeated sniffling, threatened to dredge up Bill Clinton sex scandals, and re-upped a two-decade-old fight with a Hispanic beauty queen.
Democrats were breathing easier in the aftermath of the debate, hoping Trump's repeated falsehoods and blunders will help her make the case that he's not ready for the presidency.
Republicans downplayed any impact on the deadlocked race, with several GOP senators saying they didn't even watch. About 80 million viewers tuned in Monday, making it the most watched presidential debate in American history.
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After weeks of sliding poll numbers, the debate gave Clinton a fresh set of lines on the stump.
"He actually bragged about gaming the system to get out of paying his fair share of taxes," Clinton said to the crowd at Wake Technical Community College in Raleigh on Tuesday afternoon.
"I think there is a strong probability he hasn't paid federal taxes a lot of years. And this is a man who goes around saying our military is a disaster," she said. Clinton's team said it plans to continue milking the debate.
Trump early Tuesday went on the attack. While still saying he did better than Clinton, Trump blamed his performance on "unfair questions" from moderator Lester Holt of NBC News, as well as what he deemed a faulty microphone that he said may have been tampered with.
Trump's performance is unlikely to damage his standing with his base, however, since it mirrored the unpredictable and bombastic nature that is a big part of his appeal to conservatives who are angry with the status quo. He announced late Tuesday that his campaign had raised $18 million as a result of the debate.
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Clinton's debate strategy seemed geared toward energizing women and minority voters by frequently pointing to disparaging comments Trump has made in the past.
"You had some members of the Obama coalition that weren't as enthusiastic as they needed to be," said David Plouffe, a Democratic strategist who managed President Obama's 2008 campaign. "I think she probably did a lot of good with them. It doesn't mean the race is going to change overnight."
Clinton used the last five minutes of the debate to launch what was clearly a calculated attack intended to mobilize a key piece of that Obama coalition: Hispanics. Despite Trump's dismissive attitude toward Latino voters, they've not shown the amount of support that Clinton's team has expected.
So toward the tail end of the debate exchange, she brought up Alicia Machado, a former Miss Universe winner whom Trump had called overweight.
"He loves beauty contests, supporting them and hanging around them," Clinton said on the debate stage at Hofstra University. "And he called this woman 'Miss Piggy.' Then he called her 'Miss Housekeeping,' because she was Latina. Donald, she has a name."

Trump seemed to be caught off guard.
"Where did you find this? Where did you find this?" he stammered.
"Her name is Alicia Machado," Clinton said.
By Tuesday morning, Clinton's team had put out a video featuring Machado. It detailed how Trump had threatened to revoke her crown after she gained weight.
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In a conference call Clinton's team set up later Tuesday afternoon, Machado told reporters that she had hoped to forget about the unpleasant episode with Trump.
"For me this election is like a bad dream," Machado said. "I never thought and I never imaged that 20 years later I'd be in this position — watching this guy, again, doing stupid things and making stupid comments."
Trump also focused Tuesday on the former beauty queen, but in a way that seemed to compound the damage, at least among women and Hispanics.
"She was the worst we ever had, the worst, the absolute worst. She was impossible," Trump said on Fox News Tuesday. "She was the winner and she gained a massive amount of weight and it was a problem."
Plouffe called Trump's performance in the debate "an embarrassment of riches."
"He took the bait a lot and went down these winding paths that didn't help his case," he said.
If Democrats were relieved by Clinton's evening, Republicans showed various signs of anxiousness. Some wanted to avoid the topic altogether.
Senator Marco Rubio, who had lost his home state of Florida to Trump during the GOP primary after several testy debate exchanges, said he was on an airplane and did not watch.
Mark Kirk, an Illinois Republican locked in a tight Senate race this year, waved off a reporter who approached him in the Senate basement about the debate as an aide curtly said, "We're not talking about that."
John McCain, an Arizona Republican, would only say that he thought it was "very interesting" as he hurried toward an elevator for the weekly Republican luncheon.
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Several Republican senators said they would like to see Trump be more aggressive in future performances, and focus more on Clinton's trustworthiness, the looming continued release of her e-mails, and her foreign policy record as Secretary of State.
"What he demonstrated last night was that he wasn't going to go on the attack," said Senator Thom Tillis of North Carolina, adding that Trump was able to show voters who may not have been paying attention until now that "he can act calm and methodical."
"If anything I think he held back in a few instances where maybe he should have gone on the attack," Tillis said. "But at the end of the day, he demonstrated that he can be measured."
Trump, however, signaled that he might become more aggressive in the future, and may open up new lines of attack on Clinton by focusing on President Clinton's infidelities.
Just before the debate, he had said he was going to invite Gennifer Flowers, who had an affair with Clinton in the 1970s, to the debate. Trump later backed off.
"Well, when she hit me at the end with the women," Trump said Tuesday morning during the Fox News interview. "I was going to hit her with her husband's women and I decided I shouldn't do it because her daughter was in the room. I didn't feel comfortable doing it. I think I did the right thing. It's not worth a point. I didn't feel comfortable doing it with Chelsea in the room. I think Chelsea is a fine young lady."
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Clinton, speaking to reporters on her campaign plane, shrugged off the threat, saying "he can run his campaign however he chooses.''
She got in another little dig before wrapping up with reporters.
"Anybody who complains about the microphone is not having a good night," Clinton said.
Annie Linskey can be reached at annie.linskey@globe.com. Follow her on Twitter @annielinskey. Matt Viser can be reached at matt.viser@globe.com. Follow him on Twitter @mviser. Tracy Jan can be reached at tracy.jan@globe.com. Follow her on Twitter @TracyJan.