They could stop you and Mrs Albaby (you say she's Cuban), and if you can't show you're citizens, what is to stop them from shipping you off to Nicaragua? Without due process (which appears to be regarded as nothing more than a quaint notion these days), and "papers" on your person, there is nothing stopping the Miller Goon Squads.

Are you talking about legally, or illegally?

Legally, there's no obligation for us to demonstrate that we're citizens. They can't just ship us off somewhere for failing to have proof that we are citizens. That's different from non-citizens, even lawful permanent resident non-citizens, who are legally required to have documentation of their legal status. If we are citizens and are unlawfully deported, we would have the right to submit a claim to a U.S. court (because we are citizens of the U.S., even if we are not present in the U.S.), the court would have jurisdiction to review the claim, and the U.S. would have to let us back in.

Illegally, it doesn't matter whether I'm carrying my passport or not. The federal government always has the power to ship you off to Nicaragua, and having a copy of your passport on you doesn't change that. They lack the authority to do it if you're a citizen, and the restraint on them acting unlawfully is always the prospect of after-the-fact remedies rather than any prospective limit on their physical ability to do it.

The shocked outrage in the OP article is due in part to the article author - or at least the ACLU rep quoted in it - not being aware that LPR's and other legal non-citizens are, in fact, legally required to have proof of their immigration status on them at all times. And yes, you can get a civil violation and a fine if you don't comply with that requirement. That is different than the rules for citizens, but it's been that way for decades.