Republican presidential candidate Ted Cruz is blasting rival Donald Trump for a National Enquirer story accusing Cruz of having five mistresses. Here's a breakdown of how a week of fighting got us here. (Sarah Parnass/The Washington Post)

A nasty feud that escalated Thursday between Donald Trump and his chief Republican rival over their wives set off a new wave of alarm among establishment Republicans, who fear that the GOP front-runner would drive away female voters in a general-election fight with likely Democratic nominee Hillary Clinton.

Trump’s gender problem flared again this week as he and Sen. Ted Cruz of Texas traded insults while Cruz’s wife, Heidi, became the target of vitriol on social media from Trump and his supporters. At one point, the real estate mogul retweeted an unflattering image contrasting Heidi Cruz’s appearance with his wife, Melania, a retired model.

“The images are worth a thousand words,” read the caption on the photo that Trump retweeted to his 7.2 million followers.

That message and others have prompted an outcry among Republicans and Democrats alike, while Cruz said Thursday that “real men don’t bully women.”

“Our spouses and our children are off-bounds,” Cruz told reporters while campaigning in Dane, Wis. “It is not acceptable for a big, loud New York bully to attack my wife. It is not acceptable for him to make insults, to send nasty tweets.”

A screen grab of a tweet showing Heidi Cruz, left, and Melania Trump, right, that was retweeted by Donald Trump on Wednesday.

He added: “Donald, you’re a sniveling coward. Leave Heidi the hell alone.”

The altercation underscores the striking nastiness of the GOP primary race and the uncomfortable gender politics surrounding Trump, who has a long history of making incendiary remarks about women and their appearance. Trump has shown little reluctance in attacking his female rivals — or some of his rivals’ spouses — in ways that strike many as sexist or demeaning, and many fear that the insults are a harbinger of the gutter rhetoric to come if he faces Clinton in November.

Trump has called Clinton “very shrill,” belittles her for a lack of stamina and energy, and late last year jabbed her and husband, Bill Clinton, for the latter’s marital indiscretions while he was president. In another instance, Trump said Hillary Clinton “got schlonged” in her 2008 primary fight against then-Sen. Barack Obama.

“I have some very real concerns should he become the nominee. I think it would be catastrophic for our party,” said GOP strategist Katie Packer, who leads the Our Principles PAC, an anti-Trump super PAC. “Half of the reason why I’m fighting so hard to stop Donald Trump is because I think he’s a walking, talking stereotype of a sexist misogynistic pig.”

Polling shows Trump sliding among women in recent months, hurting the GOP’s already shaky position with that demographic. Trump’s favorability numbers have decreased 10 points among women nationwide since November, to 23 percent, while his unfavorable number among women has jumped to 75 percent from 64 percent, according to a Washington Post-ABC News poll taken this month.

The changes among men have been less pronounced, with 37 percent now favorable and 59 percent unfavorable. In the states that have voted so far, Trump received an average of 41 percent of the male vote and 34 percent of the female vote.

The fight with Cruz began earlier this week when Make America Awesome, an anti-Trump super PAC, circulated ads on Facebook featuring a risque photograph of Melania Trump from a 15-year-old British GQ photo shoot. It was part of a concerted push to diminish the billionaire among values voters in Utah.

“Meet Melania Trump. Your next first lady. Or, you could support Ted Cruz on Tuesday,” the ad read.

Trump, who went on to lose the Utah caucuses, excoriated Cruz and issued a threat via Twitter: “Be careful, Lyin’ Ted, or I will spill the beans on your wife!”

Trump — who wrongly alleges that Cruz was behind the ad — defended the tweet Wednesday on Fox Business Network, saying it was a “disgraceful” and “terrible thing” that demeaned his wife, “a very, very successful model.”

Then came Wednesday night, when Trump retweeted the unflattering image of Heidi Cruz, setting off a fresh series of condemnations.

To Trump’s critics, the attacks on Cruz are just the latest in a troubling pattern of reducing women to their physical appearance and disparaging them in exceptionally personal ways.

Exhibit A is the long-running on-again, off-again feud with Fox News anchor Megyn Kelly, whom Trump called “crazy” and “average in so many ways” in a series of tweets last week. Fox News said the name-calling is part of a “sick obsession” that “is beneath the dignity of a presidential candidate.”

Sen. Lindsey O. Graham (R-S.C.), a former presidential candidate and an outspoken critic of Trump, said Thursday on MSNBC, “I’m worried that young women think that the standard-bearer of the Republican Party believes that Megyn Kelly is a bimbo.”

GOP strategists fear that Trump clinching the nomination could present an opportunity for Democrats, who are poised to choose the first female presidential nominee and who in past elections have accused Republicans of waging a “war on women” over access to affordable women’s health care, abortion rights and pay equity.

Trump’s treatment and views of women have been a central issue throughout his presidential campaign. At the first GOP debate, in August, Trump berated Kelly for asking him about past insults of women and singled out actress Rosie O’Donnell as the specific woman he referred to as a “fat pig.” A month later, Trump criticized the appearance of rival Carly Fiorina, the only woman who sought the GOP nomination. “Look at that face,” he told Rolling Stone magazine. “Can you imagine that, the face of our next president?”

Marcy Stech, communications director at Emily’s List, which has endorsed Clinton, said “the Republican base might find this amusing, but the reality is that these are just the kinds of misogynistic and outrageous comments that will cause lasting damage with women voters.”

She added: “We’ll have plenty of opportunities to remind women voters of this moment even after today’s news cycle has blown over.”

Packer said Trump’s standing with female voters could also endanger the GOP’s hold on the Senate or even the House. At the same time, Packer said, she thinks the anti-Trump movement could prevent the party from being branded by Trump alone.

“Hillary Clinton is very, very vulnerable among this group of women that she needs to have as her base: independent women, and soft Republican women. She’s very vulnerable with them today,” Packer said. “Should we nominate Donald Trump, they will flock to her because they see him as someone who’s repulsive. And it’s not just about so-called ‘women’s issues,’ it’s about how he values women and about how he’s willing to make women feel to benefit himself.”

For months Trump has defended himself against accusations of being offensive to women, saying that he hits all his challengers equally. He labeled former Florida governor Jeb Bush “low energy” and sought to diminish Sen. Marco Rubio of Florida with the nickname “Little Marco.”

“I’d hit you the same way,” Trump told NBC’s Chuck Todd in February when pressed on the issue. “I mean, you are the perfect one to ask that question — you have been, you know, under fire from me for a long time, and you are far from a woman.”

“I think there are some women — there’s one sitting right over there in the beautiful red dress. You see that woman over there? I have great respect for that woman over there,” he said, as Todd clarified to viewers that Trump was talking about veteran reporter Andrea Mitchell.

“I have great respect for that woman,” he said. “And I don’t know that she knows I’m talking about her. I’m talking about you. I would never do that to you.”

Emily Guskin, Abby Phillip and David Weigel contributed to this report.