A video posted to Ted Cruz's presidential campaign's Facebook page attacks rival Donald Trump for his opposition to North Carolina's transgender bathroom law, accusing Trump of being one of "the PC police." (Ted Cruz)

We know what the Republican presidential candidates think. Donald Trump says people should be able to "use the bathroom they feel is appropriate." Ohio Gov. John Kasich said he wouldn't have signed a so-called "bathroom bill" into law. Texas Sen. Ted Cruz says the country has "gone off the deep end" by allowing transgender people into the bathrooms of their choice, and his campaign just released the ominous video above.

But Americans' opinions on whether transgender people should be able to use the bathroom of the gender they identify with is much more murky. There just isn't a ton of public opinion polling on this issue that has so arrested America's attention since North Carolina became the first state to require people to use public bathrooms of the gender listed on their birth certificate.

We do know that people tend to support anti-discrimination laws for LGBT people — legislation like making it illegal to deny people services or housing based on their gender identity or sexual orientation. But there's also very early, anecdotal evidence that opponents to those kinds of laws have success when they zero in on what they mean for public bathrooms — specifically, how these laws would also allow transgender women to use women's bathrooms and locker rooms.

Here's what little data we have on this, thanks to The Washington Post's polling guru, Scott Clement:

A majority of Democrats, Republicans and independents think a child should be required to use the bathroom of their birth gender, according to a two-year-old CBS News poll.

In Houston, an ordinance to ban discrimination of LGBT people got soundly defeated after opponents put bathrooms front-and-center; 61 percent voted against it, and 39 percent voted for it.

In North Carolina, almost half of residents — 49 percent — say states should prohibit cities from passing ordinances that open up bathrooms to transgender people, according to a new Elon University poll. Such numbers would seem to at least somewhat vindicate North Carolina Gov. Pat McCrory (R), who's taken a lot of heat from the business, media and entertainment communities for signing the nation's first bathroom bill into law.

But then we turn to South Dakota, where another Republican governor, Dennis Daugaard, vetoed a bathroom bill while making a conservative case to leave the issue alone — and did so without too much backlash.

Clearly, we need more evidence before we can say what direction America's leaning on this. But that's going to take time.

Bathroom bills are a relatively new thing in the legislating world. They seem to have suddenly proliferated alongside religious protection bills this year — likely a reaction to the Supreme Court legalizing gay marriage in June and a renewed interest on both sides on LGBT laws. There's also the Caitlyn Jenner factor, which has made transgender people much more visible. (Trump said Thursday on "Today" that Jenner could use any bathroom in Trump Tower.)  A dozen or so states are considering their own bathroom bills.

Because we're still so early in this debate, there's lots of room for any nascent narrative about bathroom bills to change. It's somewhat ironic that all this is dominating the headlines despite the fact very few Americans say they know someone who struggles with which bathroom to use.

A June 2015 Public Religion Research Institute survey found just a third of people said they didn't have a close friend or family member who is gay or lesbian, but 85 percent said they didn't have a close friend or family member who is transgender.

That's a critical missing link in the bathroom debate. As we've documented, Americans' familiarity with gay people was a huge contributing factor in reshaping public opinion over gay rights in favor of same-sex marriage so quickly.

As more Americans get to know transgender people, will we see a similar shift in how the country feels about their bathroom rights? It's too early to say, but with politicians weighing in, the American people will begin to as well.