Here’s my wild conspiracy theory: the choice of Fiorina and announcing it now came from the Republican establishment, not Cruz. With his unpopularity, Cruz has an uphill fight to beat Trump even in the open convention scenario. So the RNC convinced him to select Fiorina now, and then if Trump isn’t chosen in the first round at the convention, Cruz gracefully bows out and promotes her as the candidate instead. Having her as the VP now gets her name out there for a few months before the convention, and (slightly) weakens arguments that any candidate has to have already been in the running. She was the choice because the RNC sees her as the most viable candidate to oppose Hillary. Cruz is going along with this because he has been promised some quid pro quo for taking one for the team.
Of course, this would suggest more strategy and cohesiveness than I think the Republicans currently possess. And it’s ridiculous. But still…
When Clinton was accused of playing the “woman card”, she had the great response of “Well, if fighting for women’s health care and paid family leave and equal pay is playing the woman card, then deal me in.” I don’t know of anything like that that Fiorina could say. I’m guessing something about how she fights Planned Parenthood and protects women and babies from them.
Or maybe, they think that Fiorina, the former CEO of HP, could give Cruz a boost in California, especially in the northern districts that are strongly Democratic anyway; every district Cruz wins is three fewer delegates Trump gets on the first ballot.