"I was lazy and my Mom had to say, 'Go practice!'" she told Sunday Morning correspondent Anthony Mason.
One reviewer called her music "moving to a degree that's practically paralyzing." Spin magazine called her latest album "as addictive as ice cream dots." When she played the late night talk shows, Conan O'Brien told her she gave one of his favorite performances in a long time — and English isn't even her first language. She was born in Moscow and left the Soviet Union in the last years of the Cold War.
"I don't know, to me I truly express myself in English," she said.
Her mother, a music teacher, and her father, who played violin, started her musical education early. Then when Spektor was 9, perestroika opened a door to the West and her family decided to go through it. They landed in the Bronx.
"It was an adventure," she said. "You know they make movies about this stuff. We didn't know anybody here."
She also had to leave behind the family piano. She felt lost without it.
"I had a really hard time," Spektor said. "I was practicing on window sills and tables. I just was missing the whole connection to it."
Finally she discovered a piano down the street in the basement of a Bronx synagogue, and used it to practice. The same piano is still there. Spektor took Mason to see it.
It was on the synagogue stage that Spektor gave her first American recital. A student of classical music, she never aspired to write songs herself.
"When you're playing such brilliant music every day, then the last thing you ever want to do is try to write something of your own that's crude and not as good," she said.
But songs seem to just flow to her — like the tune she improvised during a break from the interview as she waited on her grandparents' balcony.
She uses her swooping voice to play with words and sounds with an immigrant's unrestrained enthusiasm for her adopted language. She said she simply likes to mess around.
"It's fun," she said. "It's a statement to yourself to be free."
Spektor started out singing solo in cafes to small but spellbound audiences. Word spread. The secret is now out. Now you hear her songs in the soundtracks of tv shows like "Grey's Anatomy" and "CSI: New York." That show's creator, Anthony Zuiker, is one of her biggest fans.
"That music completely transported me and touched me in such a way that more of the world should hear this music," he said, "and I put her on the show right away. And I will continue not only to put her music on my show, but also have her on the show personally. I already have a story line worked out. And she'll probably make her debut on 'CSI: New York' for season four."
But Spektor is still suspicious of success.
"My grandparents turned 18 and World War II happened the next day," she said. "So I have that very Russian-Jewish thing of 'Tomorrow you might get a phone call about something wonderful and you might get a phone call about something terrible.'"
Lately the news has all been good. On her latest tour Spektor sold out two shows at New York's Town Hall.
"In my hometown," she said. "It's so touching, you know? I try not to thinking about it 'cause it's just — it's too good."