Indianapolis (CNN) Ted Cruz is aiming to take advantage of Donald Trump's controversies with women -- including his sparring with Hillary Clinton -- to capture the Indiana primary.

That messaging was front and center Wednesday as Cruz announced his selection of Carly Fiorina as his running mate, the culmination of weeks of overtures to female voters.

"Over and over again, Carly has shattered glass ceilings," Cruz said as he introduced Fiorina in Indianapolis.

Thursday, Cruz went directly after Trump.

"Donald has a problem with strong women. This is not subtle, it's not complicated: he has a real problem with strong women. It's one of the reasons he cannot win a general election," Cruz told reporters.

The stakes could not be higher for Cruz, who trails in the delegate count and needs a win soon to stop Trump's momentum towards the 1,237 needed to clinch the GOP nomination.

Cruz has put particular emphasis on drawing contrasts with Trump leading up to Tuesday's primary, and female Republican voters could be key to a Cruz victory.

Trump has a history of controversial comments toward women, both before and during his presidential campaign. Tuesday, celebrating his five-state victory over Cruz and John Kasich, Trump went after Clinton.

"I think the only card she has is the women's card," Trump said. "She has got nothing else going. Frankly, if Hillary Clinton were a man, I don't think she would get 5% of the vote. And the beautiful thing is, women don't like her."

Cruz frequently mentions his wife, Heidi, a successful Goldman Sachs businesswoman, on the trail. Heidi is proof that "strong women can accomplish anything in the United States of America," he said after his Wisconsin win earlier this month.

He describes his mother, Eleanor, as a "pioneering computer programmer."

This week, as Heidi Cruz campaigned on his behalf in Nebraska, the Texas senator brought daughters Caroline, 8, and Catherine, 5, along as he went on a bus tour across Indiana. He rewarded them with a stop at a local ice cream shop.

"When mom's in Nebraska, their eating goes a little downscale," Cruz said, pausing to tuck a napkin in Catherine's shirt.

The campaign acknowledges the contrast Cruz is working to draw with Trump on women.

"At the end of the day, Donald Trump alienates women at a tremendous rate, while at the same time Ted Cruz is someone who identifies and looks for opportunities to include women in the campaign in every way possible, and you see it with Carly Fiorina, the prominent role of Heidi in the campaign on the campaign trail, and of course, his two wonderful daughters," said national spokesman Ron Nehring.

Cruz cast himself as a feminist at his "Women for Cruz" coalition rollout in March: "Women are not a special interest. Women are a majority of the United States of America and every issue is a women's issue," Cruz said.

Cruz's selection of Fiorina as a running mate underscores that outreach, and he referenced her gender throughout his announcement.

"Carly is brilliant and capable and, yet, she experienced the hard-scrabble world of being a woman professional in a business world that extracts a price," Cruz said Wednesday.

Fiorina herself waded into the "woman card" debate, telling CNN's Sunlen Serfaty she would never ask people to vote for her because of her gender.

"I am very proud to be a woman," she said. "But I would never ask people to vote for me because I'm a woman. Ted Cruz didn't pick me because I'm a woman, Ted Cruz picked me because I'm a capable individual."