Milwaukee (CNN) Tuesday's Wisconsin primary is the best chance for Republicans to deal Donald Trump a major loss just before the race shifts to East Coast states where he's expected to dominate.

But it comes after his rockiest week yet on the campaign trail, with Trump -- so far made of Teflon, seemingly immune from the ill effects of the controversies he's triggered -- at risk of suddenly looking vulnerable, particularly after reversing himself several times within 72 hours on issues related to abortion.

Mathematically, Wisconsin won't make or break Trump's path to the Republican nomination, but a loss here could make it much harder for the Republican front-runner to clinch the party's nomination.

"The conversation's going to be, 'This is going to go to an open convention.' I think you're going to see that discussion really go through the roof," said Ed Goeas, a Republican pollster and chief strategist for the anti-Trump Our Principles PAC.

Wisconsin should be Trump Country: His trade-bashing, blue-state, working-class appeal in manufacturing states like this one is at the core of his case he can win in November.

But days before the state's Tuesday primary, polls show him trailing Texas Sen. Ted Cruz -- and with Ohio Gov. John Kasich not far behind.

His path to 1,237 delegates was already precarious. Then Trump stepped into two abortion controversies -- suggesting women who undergo the procedure should be punished if abortions were outlawed, and then saying current federal policies should stay the same, both stances his aides quickly reversed in statements. It has put him at risk of losing more female supporters -- with Wisconsin posing the first test.

Wisconsin has 42 delegates on the line. Of those, 18 go to the statewide winner, while the other 24 are divvied up three apiece to the winner of each of Wisconsin's eight congressional districts.

Even by winning all 42, Cruz wouldn't make it impossible for Trump to win the 1,237 he needs to clinch the party's nomination before its convention in Cleveland, where there will also be a pool of unpledged delegates available to every candidate.

But a Cruz win would have two tangible effects on the race.

Increasingly, the inside-baseball games would matter more -- an advantage for Cruz and Kasich over Trump. From the attention to detail that allowed Cruz to net 10 more delegates than Trump in Louisiana, despite the real-estate mogul winning there, to the legal ramifications of disavowing his pledge to back the eventual GOP nominee in South Carolina, the quirks of each state's rules would become critical to a Trump campaign that has eschewed those intricacies.

Wisconsin is also a confidence game. It plays an oversized role in the GOP contest because it's the only major contest in a four-week stretch. A big Cruz win pokes another hole in Trump's inevitability, lending Trump's opponents -- and the donors backing the right's stop-Trump efforts -- a sense that they could win the fight.

Trump's campaign is contending to win Wisconsin, and says it views the state as a toss-up. Yet his aides are downplaying the effects of a loss there.

"We want to win every delegate everywhere, so every loss is disappointing. But it's not one of our must-win states," said Barry Bennett, a senior adviser to Trump's campaign.

He said he has modeled a path to 1,450 delegates for Trump that included zero from Wisconsin.

"I conservatively couldn't count on it for anything. My crystal ball does not work there," he said, arguing that while areas like Janesville do reflect Midwestern states Trump has already won, Milwaukee tends to vote more like Chicago, while Madison is a college town that's difficult to project.

On to the Empire State

Bennett also pointed to the race's move to the East Coast -- New York is next on April 19, followed by Pennsylvania, Maryland, Connecticut, Delaware and Rhode Island the next week -- as a big opportunity for Trump to rack up delegates.

"I love cheese curds and beer as much as the next guy, but New York two weeks later, we're already over 50%, which means we win all 95" delegates, Bennett said.

Goeas, though, sees Wisconsin as a critical stage in the race.

Trump's string of controversies around women -- from his Twitter insults of Heidi Cruz's looks to his comments about abortion -- have alienated female voters and sent the intensity of the one-third of the GOP that is dead-set on stopping Trump soaring to match the one-third that is with him no matter what, Goeas said.

That puts Trump in a bind: If he's not crushing his competition, he can't back away from the bombastic rhetoric he's employed for the last year -- otherwise, he'd risk losing his own supporters.

But the longer he uses such language, the more hardened and intense the resistance becomes.

Either way, Trump's long-term viability -- for the Republican nomination, or in the general election -- would suffer.

"He has to stay with his image he has, the way he campaigns, because if he starts taking his foot off the pedal at all, he then loses enthusiasm with his third," Goeas said. "It puts him in a box."

The contest comes after one of Trump's most difficult weeks on the campaign trail.

Still under fire for retweeting an unflattering picture of Heidi Cruz, and facing high disapproval ratings among women, Trump stepped into another controversy on Wednesday in a town hall interview with MSNBC's Chris Matthews.

Asked about abortion, Trump said that women who undergo the procedure should face "some form of punishment." Within hours, his campaign had released a statement reversing his position -- but it was too late to tamp down criticism from both those who oppose abortion rights, who generally see women as victims of the procedure, as well as those who support abortion rights.

Then, two days later, Trump set off another controversy when he told CBS that abortion laws should not change on the federal level -- another position that forced his campaign to backtrack later in the day, issuing a statement saying Trump only meant until he's president and can appoint judges who see abortion as a states'-rights issue.

"I don't know that it's been the worst week of my campaign," Trump said on CBS' "Face the Nation" in an interview aired Sunday. "I think I've had many bad weeks and I've had many good weeks. I don't see this as the worst week in my campaign."

If Friday night at the Republican Party of Milwaukee County's fish fry was any indication of Trump's fortunes in Wisconsin, he has an uphill climb.

Cruz -- who'd been introduced by the state's popular governor, Scott Walker -- eviscerated Trump's foreign policy positions, saying they call into question Trump's "fitness and judgment to be commander in chief."

"Nominating Donald Trump elects Hillary Clinton. Hillary not only wins, she wins by a big margin," Cruz said.

Palin gets rough reception

Sarah Palin, the former Alaska governor and Trump surrogate, was on hand to make Trump's pitch, but she received a chilly reception. Palin received polite applause, but it paled in comparison not just to Kasich and Cruz but to local broadcast personalities who spoke in between candidates.

Palin lambasted the GOP establishment, saying the country needs a break from "the same old politicos and insiders who betrayed us over and over again" and declaring: "Enough of the holier-than-now lectures from those steering us into rocky shores."

And she made the case that Trump's positions aren't detached from the Republican platform, comparing his anti-trade stances to Ronald Reagan.

She also took a shot at Cruz, arguing that he's soft on trade.

"You have to ask yourself, who is this? It's not someone who understands Ronald Reagan," Palin said.

But when Palin pitched "Donald Trump's positions," a man in the audience jeered: "What positions?"