An hour into Betty Buckley’s first set at Joe’s Pub, she began the aching ballad from “Cats” that has won her legions of fans. Among them, she now knows, is President Trump.

Ms. Buckley, 77, who regularly reposts social media content critical of the Trump Administration, did not mention the president when she tore into “Memory,” which brought the reverent Thursday evening crowd to its feet, whistling and whooping. She didn’t mention him when she finished the number, either.

But then she pivoted to Paul Simon’s “American Tune” — with lyrics like “I don’t have a friend who feels at ease” and “I wonder what’s gone wrong” — and called it “particularly perfect for what’s happening these days, which is weird, and not cool.”

This has been an odd few months for Ms. Buckley, who has known for years that Mr. Trump loved “Memory,” but did not know her version, from the 1982 Broadway production, made her his favorite Grizabella, the once glamorous but now shunned feline whose plea for connection is the musical’s emotional high point.

“I didn’t know he knew my name,” Ms. Buckley said of Mr. Trump. “It left me really gobsmacked that my name actually resides in his consciousness.”Credit…Graham Dickie/The New York Times

How does she know now? Well, in March, Mr. Trump reminisced about seeing Ms. Buckley in that Andrew Lloyd Webber show while addressing the board of the John F. Kennedy Center for the Performing Arts, where his handpicked trustees had appointed him chairman. “The place went crazy,” he recalled of the “Cats” performance, before musing, “Is Betty Buckley still alive?” He continued: “Of all the great voices and stars, bigger stars than her, she had the best voice.”