At the time she had left the show but was asked to return.
Fey said: “I wasn’t sure. I know I looked a little like her but I also knew someone like Kristen Wigg could have done with ease.”
But for six weeks, it made her famous.
She added: “So many people watched it and recognised me. They’d come up to me in the street.
“A French newspaper even ran a picture of me and Amy Poehler as Hillary Clinton, thinking we were the real people.
“At the end of it all, it started to get a little scary, and then it piqued when Sarah Palin appeared on the show.”
In April it was announced that the UK would launch its own version of the long running sketch show, produced by the US show’s creator Lorne Michaels.
Graham Norton, who shared the festival stage with Fey, said he didn’t believe that British writers would stay up all night on a Tuesday, as they do in the US, to finish scripts in time for the Wednesday read through.
But Fey said: “Here’s a dirty secret. You don’t have to do it that way. You could start in the morning.”