"Well, of course," Romney said when asked on the campaign trail in Pennsylvania. "Of course I'd have women in Augusta. Sure."

Press Secretary Jay Carney said Thursday that the president's "personal opinion is women should be admitted."

"We've kind of passed the time that women should be excluded from anything," Carney said.

Newt Gingrich's wife, Callista, tweeted Thursday that she'd "love" to belong to the club.

Gingrich sent out a tweet supporting that idea shortly thereafter.

Augusta's rule to only accept male members has long been controversial, but gained additional notoriety this year after Masters sponsor IBM appointed a new, female CEO. The club has traditionally extended membership offers to the heads of the primary tournament sponsors.