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After his overwhelming win in the Wisconsin Republican primary Tuesday, Ted Cruz is claiming a "turning point" in the GOP race which he believes could propel him to victory – though the conservative firebrand faces some tough challenges ahead.

“I'm so encouraged after what was a terrific victory ... in Wisconsin,” Cruz said Wednesday. “It was a turning point, I believe, in this entire election. It culminated four states in a row in the last two weeks where we have beaten Donald Trump over and over again.”

Cruz indeed bolstered his case that he's gaining momentum in the battle against front-runner Trump. He scored 48 percent of the vote to Trump's 35 percent, and picked up the lion's share of the state's delegates. Ohio Gov. John Kasich trailed far behind.

Cruz's path to winning the nomination pre-convention remains virtually non-existent. But some analysts saw Cruz's win as a sign that Trump needs to rethink his approach if he wants to avoid the more likely scenario of a contested convention.

The primary came after a tough week for the Republican front-runner. He was embroiled in controversy over retweeting an unflattering image of his rival's wife Heidi Cruz; he had to walk back comments he made on abortion; and his campaign manager was charged with misdemeanor battery after grabbing a reporter at a campaign event.

In a statement after the primary, Trump’s campaign sought to downplay the defeat, arguing he has “withstood the onslaught of the establishment yet again.”

“Lyin’ Ted Cruz had the Governor of Wisconsin, many conservative talk radio hosts, and the entire party apparatus behind him,” the statement said, before arguing that Trump is the only candidate who can secure the delegates needed to win the Republican nomination.

Exit polls in Wisconsin highlighted concerns about Trump from some areas of the Republican Party. A majority of GOP voters said they're either concerned about or scared of a potential Trump presidency.

But Cruz's surge could be short-lived.

Despite the win, the next few primaries are looking like slim pickings for the Texas senator, and could produce big wins for Trump. The race heads next to New York state where Trump holds a commanding lead in the polls and is the overwhelming favorite to win the primary on April 19 -- and a majority of the 95 delegates up for grabs.

A Monmouth University poll released Wednesday showed the New York real estate tycoon with 52 percent of the likely Republican vote, with Cruz at the back of the field.

The poll shows Cruz with 17 percent, behind Ohio Gov. John Kasich, who has 25 percent of the vote, despite winning only his home state and mathematically out of the delegate race.

If Trump stays above 50 percent on Election Day, he would be awarded all 59 bound delegates.

“If this result holds in every single congressional district, Trump will walk away with nearly all of New York State’s delegates,” said Patrick Murray, director of the independent Monmouth University Polling Institute.

The poll was conducted by phone from April 3-5.

Another major state coming up is the June 7 primary in California. Once seen as safe Trump territory, a new poll by SurveyUSA shows Trump with just an 8-point lead over Cruz. With 172 delegates up for grabs, California could be a deciding factor if Cruz is able to keep building momentum.

Only Trump has a plausible path to lock up enough delegates before the convention, but it's an increasingly slim one. To claim the nomination by the end of the primaries on June 7, he'd have to win 57 percent of the remaining delegates. So far, he's won just 46 percent.

As of Wednesday afternoon, Trump had 743 delegates. Cruz had 517, and Kasich had 143. It takes 1,237 to win.

The Associated Press contributed to this report.