Defeat in the north-central state isn't likely to immediately change the course of the overall nominating contest, but it could serve as an indicator of the race's current status ahead of the New York primary on April 19, where polls show both in the lead.
It's been a bumpy period for Trump, the Republican billionaire from New York.
Although his campaign has seemed bulletproof up until now, his latest controversies -- including abortion, opponent Ted Cruz's wife and a journalist who said she was roughed up by Trump's campaign manager -- have alienated women voters further, polls indicate.
With polls for the Wisconsin Republican primary showing the ultraconservative Cruz holding a 10-point lead, Trump has launched a series of events in the heartland state to rally support. Moderate John Kasich, the Ohio governor, is polling third and last.
Campaigning in Wisconsin yesterday accompanied by Sarah Palin, Trump attacked Cruz for failing to report a loan from Goldman Sachs, his wife's employer.
"Sometime you're better off saying, wait a minute. We're defending Japan. I mean what we're doing is costing us a fortune," he told the Fox News Sunday programme.
"And not only Japan, (but) South Korea. We have 28,000 soldiers on the line," said Trump, who said that rather than fully reimbursing the US for their defense "they pay us peanuts."
He added: "Maybe they would, in fact, be better off if they defend themselves from North Korea... Including with nukes."
Currently, Trump has 739, Cruz 460 and Kasich 145. To win the Republican nomination outright, a candidate needs 1,237.
