NEW YORK — Hillary Clinton and Donald Trump both earned redemption from their home state Tuesday night, with New York-sized victories that supplied a needed boost to each of their campaigns.
On the Democratic side, Clinton hadn't prevailed in any state in nearly a month before New York voted. So her win, by double digits with 96 percent of the vote counted, helps reassure party leaders that her candidacy is on course.
Bernie Sanders, the Vermont liberal who never abandoned his New York accent, was let down by voters here. He will now need to win the next few contests with overwhelming victories to make up his deep delegate deficit.
"Today you proved once again, there is no place like home," said Clinton, her voice cracking at her victory party at a Sheraton hotel in midtown Manhattan.
She added a prediction: "The race for the Democratic nomination is in the home stretch, and victory is in sight."
Sanders returned to Vermont as Clinton was declared the winner. "I miss Vermont, and we need to get recharged and take a day off,'' he told local reporters, according to the Burlington Free-Press.
For Trump — the brash New York developer whose campaign was launched 10 months ago with a slow ride down an escalator in Trump Tower — the victory was not only significant, but sweet.
About 30 minutes after the race was called, Trump strolled before supporters at Trump Tower to the strains of the Frank Sinatra song "New York, New York" and thanked "the people who know me best.''
"I could think of nowhere I would rather have this victory," Trump said, with throngs of reporters filling the ground floor of his gilded building in midtown Manhattan.
"We don't have much of a race anymore," he declared. Senator Ted Cruz "is just about mathematically eliminated."
Cruz now has no mathematical chance of gaining the number of delegates needed to win the GOP nomination outright. And the New York result gives Trump a better chance — if he wins a series of mid-Atlantic states voting next week — of capturing the nomination and avoiding a fight at the Republican National Convention in Cleveland in July.
Heading into Tuesday's primary in New York, Trump needed about 69 percent of the remaining bound delegates to secure the nomination. If he wins all the delegates in New York, he would need about 64 percent going forward. There are also several hundred unbound delegates up for grabs, which the campaigns are now trying to woo to their side.
Trump's victory comes after weeks in which Cruz beat him soundly in Wisconsin on April 5 and outmaneuvered him in the complex system of delegate math for the convention.
Though not all returns were in, he would carry every delegate available in New York if he topped 50 percent in each congressional district.
But Cruz has proven more adept at identifying supporters and ensuring that they are on the slate of delegates selected at state conventions. In some instances, those delegates are bound to vote for Trump on the first ballot at the convention. If Trump doesn't secure a majority, those delegates would be released to vote for whomever they want on subsequent ballots.
Trump has made inroads with his argument that the convention rules for delegates are unfair and that the nominee should be the candidate who gets the most votes in the primaries, even if he does not secure the 1,237 delegates required to clinch on the first convention ballot. That simple message is pitted against the more complicated argument of the stop-Trump movement, which must explain why someone other than the top vote-getter should be bestowed with the title.
Exit polls in New York found that 72 percent of Republican voters think the person with the biggest share of the popular vote should be the nominee if no contender arrives at the convention with a majority.
"Nobody should take delegates and claim victory unless they get those delegates with voters and voting. And that's what's going to happen,'' Trump said after his victory Tuesday. "You watch. Because the people aren't going to stand for it. It's a broken system, it's a system that's rigged. And we're going to go back to the old way. It's called, you vote, you win."
Cruz spent the day in Pennsylvania, hunting for a slice of the delegates next week.
"Now it is our turn," Cruz told supporters in Philadelphia. "This generation must first look inward to see who we really are, after years of being beaten down. . . . I call on you, as JFK did in the '60s. And as Reagan did in the '80s, to chart a new American journey forward."
Trump — who for decades has been a fixture in New York's real estate, tabloid, and entertainment culture — started with a large lead in the state and never relinquished it. The state proved to be an ideal match for a campaign that has struggled with grass-roots organization but has thrived in places driven by media exposure and large rallies.
Cruz and Governor John Kasich of Ohio gamely made attempts at cracking into Trump's home-state lead, with visits to delis and churches in the Bronx, but in the end they got little more than Bronx cheers.
Trump also exploited a remark that Cruz made earlier in the campaign — when he ridiculed Trump's "New York values" — for maximum impact.
"New York values were on display for all to see in the aftermath of 9/11 — a strike at the heart of our city and our nation," Trump said last week during a state Republican Party dinner. "In our darkest moments, as a city, we showed the world the very, very best in terms of bravery and heart and soul that we have in America."
The results Tuesday night mean that all of the candidates have now won their home state. But in Kasich's case, his home state of Ohio is all he has won.
On the Democratic side both candidates took great pains to highlight their ties to New York. Clinton crisscrossed the state, running essentially on her Senate record of securing jobs upstate and improving schools in the Bronx and elsewhere.
Clinton's campaign team hosted a filing center for reporters and threw a party at the Sheraton hotel in Times Square. In past contests, where she lost or where results were tighter, her campaign simply issued a press release.
Speakers blasted "Empire State of Mind" by Alicia Keys and Jay Z before Clinton took the stage. She reminded the audience that she's prevailed in contests across the country, but Tuesday's victory felt different.
"This one's personal," Clinton said. "New Yorkers, you've always had my back. And I've always tried to have yours. Today we did it again and I'm deeply, deeply grateful."
The campaign vibe in Clinton's home state included something that's been missing in her campaign — outwardly at least: Joy. On Sunday she visited all five boroughs of New York City. She even violated her self-imposed rule of never eating in front of the press and gobbled an ice cream concoction specially made for her. The name of the dish: Victory.
She even (possibly accidentally) channeled Beyonce, telling a New York radio host that she carries hot sauce in her purse. Many thought it was a reference to a line in the singer's new hit song "Formation," which includes the lyric: "I got hot sauce in my bag, swag."
Sanders did put some New York attitude into his campaign here, irritating Clinton aides by amping up his attacks on her. Brian Fallon, a Clinton spokesman, told reporters he wants Sanders to dial back the rhetoric in the next set of states.
Sanders opened his rally Monday evening by highlighting the deteriorating relations between the two camps.
His campaign issued a letter to the Democratic National Committee complaining that DNC funds were being improperly used to pay Clinton staffers. It's a charge that the Clinton campaign flatly rejects.
Sanders has veered slightly away from the talking points he's been using on the campaign trail for a year and began touching on more local issues.
But the main themes of his campaign were never too far from his mind.
"You all look beautiful," said Sanders said Monday night. "You all look like you want a political revolution."
The campaign now turns toward five states next week: Connecticut, Rhode Island, Maryland, Pennsylvania, and Delaware. Trump leads in the polls in all of those states. Clinton has an advantage in Maryland and Delaware, which both have large African-American communities. Sanders is expected to do better in the New England states and hopes to make inroads in Pennsylvania, where Clinton leads in the polls.