That's not to say people like Cruz aren't useful. Trump has hired quite a few of them.
Here is a little history of the word pussy. It almost certainly started likening a woman to a pussycat in the 19th century or earlier. The phrase pussyfooting around, which appears around 1900, implied being timid, afraid, like a cat. No sense of woman there.
Pussy was in use in theater circles by the late 1940’s to mean a homosexual male. Interesting how these terms morph from women to homosexual males, much like a faggot. I don’t think Trump hired any homos. Pussycats? Hmmmmm.