MILWAUKEE — In the wake of Wisconsin, Ted Cruz, Donald Trump, and John Kasich are beginning months of trench warfare for Republican delegates, which could culminate in a wide-open, contested convention in July.

While Cruz and Trump predicted they would eventually rack up the 1,237 delegates needed to win the GOP presidential nomination, Cruz's double-digit win in Wisconsin leaves daunting math for both candidates.

"Either before Cleveland — or at the convention in Cleveland — together we will win a majority of the delegates, and together we will beat Hillary Clinton in November," Cruz told supporters in Milwaukee in claiming his Wisconsin win.

The Trump campaign, which still leads Cruz by more than 200 delegates, said the businessman will build that lead in upcoming contests in New York and other northeastern states. In a statement after the Wisconsin vote, the campaign said Trump "is the only candidate who can secure the delegates needed to win the Republican nomination and ultimately defeat Hillary Clinton, or whomever is the Democratic nominee."

If Trump fails to win on the first ballot at the July 18-21 convention in Cleveland, delegates become unbound and the race could be thrown open to other candidates.

In the meantime, Cruz, Trump and Kasich look to the next major date on the Republican calendar: April 19, when New York — Trump's home state — holds a primary.

As anti-Trump organizations work to block a first ballot victory for the businessman, his loss in Wisconsin makes it harder for him to clinch the nomination ahead of time.

"Our estimate would now project him to get 1,179 to 1,182 delegates total, or somewhere between 55 and 58 short of the 1,237 he’d need to clinch the nomination," the website FiveThirtyEight reported.

The Associated Press currently gives Trump 743 delegates to Cruz's 517. Kasich has 143 delegates and former candidate Marco Rubio still holds 171, meaning that non-Trump candidates have more delegates overall than the New York businessman.

Trump must win 57% of the remaining delegates to lock up the nomination before July — though Cruz will need to win more than 80% to do the same thing.

Different news organizations have different delegate counts, and complex rules in different states mean that some delegates' commitments may be in doubt, in a race where even a few votes could be decisive.

In addition to primaries and caucuses, the Cruz campaign is also hunting delegates at various state Republican conventions. Citing success at a recent meeting in North Dakota, the Cruz campaign plans more lobbying this weekend at a Republican convention in Colorado.

Describing Wisconsin as a "turning point," Cruz, a Texas senator, told backers that Republican voters will increasingly turn to him as the alternative to Trump.

"Three weeks ago the media said Wisconsin was a perfect state for Donald Trump," Cruz said. "But the hard working men and women of Wisconsin stood and campaigned tirelessly to make sure that tonight was a victory for every American."

The Trump campaign, meanwhile, described Cruz as nothing more than a tool of anti-Trump organizations.

While Trump himself did not comment as the Wisconsin results came in Tuesday, his campaign issued a harsh statement, saying that "Cruz is worse than a puppet — he is a Trojan horse, being used by the party bosses attempting to steal the nomination from Mr. Trump."

On Wednesday in New York, Cruz visits a charter school in the Bronx and a Christian academy in Scotia.

Trump, meanwhile, hosts a rally Wednesday night in Bethpage, N.Y.

While protesting attacks from Cruz, radio talk show hosts in Wisconsin, anti-Trump political action committees, and members of the Republican establishment, the Trump campaign predicted wins in New York and beyond.

On April 26, a week after the New York primary, five more northern and eastern states pick Republican delegates: Pennsylvania, Connecticut, Delaware, Maryland, and Rhode Island.

Kasich, Ohio's governor, is predicting an open convention, and plans to tout his ability to win a general election as he campaigns in New York and other northeastern states on the upcoming primary schedule.

While both Cruz and Trump have called on Kasich to exit the race, the governor and his aides said neither of his opponents will be able to clinch the nomination before the convention.

In a campaign memo, Kasich strategist John Weaver said of Cruz and Trump: "Rather than admit their own electoral and political shortcomings, they are blaming John Kasich, the only Republican who can defeat Hillary Clinton in November."