There's a great scene in the 1995 film The American President, a romantic comedy about a sitting U.S. president's foray into the dating world, in which Michael Douglas, who plays the president, tries to order flowers over the phone for his girlfriend. Douglas's character doesn't carry any credit cards and the flower salesperson thinks he's a prank caller, not really the U.S. president. What about Barack Obama? Does he have a hard time ordering things over the phone from salespeople who are understandably suspicious that they're getting a call from the U.S. president? Intrepid journalist Ryan Seacrest asked about this during a hard-hitting presidential interview, as chronicled by Politico's Amie Parnes.
Asked if he has a hard time ordering flowers — as the Michael Douglas character did in "The American President" — Obama said, "The truth is, actually, I get to keep my credit cards, and if I want to go to the florist, I could order some flowers and pay for it." (He did add that if he tried to order the flowers by phone, "they might not believe me.")
Prolific economics blogger Tyler Cowen reads this and asks, "What could you say to prove, over the phone, that you are the President of the United States?" He suggests a complicated trivia game wherein the clerk asks Obama rapid-fire questions to ascertain whether he is who he says. But, ultimately, Cowen suspects Obama would not encounter as much skepticism as one might expect.
Plus you are dialing from a 202 area code and you sound like President Obama (because you are President Obama), whose voice is well-known and distinct. I would think he would have an especially easy time establishing his identity over the phone. Furthermore the audience, wondering that maybe you are the President of the United States, would fall into the deference mode, even if some residual doubt remained.
Impersonating the President of the United States might draw interest from the law, or at least an inquiry, and that would discourage potential pranksters and make your claim more credible.