Was a Brit Mila the only thing stopping McCain from becoming a Jew?

According to 'New York Times' article, McCain quipped he would convert to Judaism - until ex-Senator Lieberman brought up circumcision.

US Senator John McCain 370 (R) (photo credit: Kevin Lamarque / Reuters)
US Senator John McCain 370 (R)
(photo credit: Kevin Lamarque / Reuters)
John Mcain was apparently considering converting to Judaism - that is, until former United States Senator from Connecticut Joe Lieberman told him he would have to have a brit mila (circumcision).
According to an anecdote included in an in-depth New York Times profile on the senior Republican senator, McCain quipped that he was converting to Judaism during an event held in honor of Lieberman after he left the Senate.
The Times quoted McCain as saying: “Everyone was saying Joe’s the most wonderful guy, the usual crap you hear. So I got up, I was the last guy, and I say: ‘I’m here to announce that I’m converting to Judaism. Because for all these years with Joe, I’ve had to eat that crappy salmon. I had to ride the damn Shabbat elevator. I’ve observed Shabbat to a point where I couldn’t even ride in a goddamn car. I’ve had all of the bull associated with this religion, and I’ve gotten not a single benefit. So I’m converting to Judaism.’”
According the account, Lieberman swiftly put an end to his short-lived plans, retorting that he would first have to have "a proper bris."