Rudy Giuliani: Obama's changes on same-sex marriage takes Romney's reversals "out of the election"

(CBS News) Former New York City Mayor Rudy Giuliani said on "CBS This Morning" Thursday that President Obama's shift from defining marriage as between a man and a woman to supporting same-sex marriage takes changes in positions of his likely opponent, Mitt Romney, "out of the election."

The 2008 Republican presidential candidate made the comment a day after Mr. Obama affirmed his support of same-sex marriage in a nationally televised interview days after Vice President Joe Biden voiced his support for same-sex marriage.

Giuliani told Erica Hill and Charlie Rose that Mr. Obama's statement Wednesday to ABC News directly conflicts with his position in 2008 that he defined marriage as between a man and a woman, which was then a reversal from his support in 1996 for legalizing same-sex marriage.

"It's going to be very hard for the president to say, 'Oh my goodness, you know, Mitt Romney changed his position on pro-choice, pro-life,' whereas he's changed his position now dramatically on, on gay rights going back over a 10-year period, so maybe in this sense it helps Romney because it takes that issue out of the election," said Giuliani. "[It] can be hard for Obama to criticize him for being a shifter on positions when this is a major shift."

Giuliani doubted Romney would shift from making the election about the economy to focusing on same-sex marriage.

"This is not something he's going to make a big issue out of, and he shouldn't," said Giuliani. "I think it's going to work for or against the president on its own. Republicans should stay the heck out of it."

While polls show that the nation is evenly split on same-sex marriage -- a recent Gallup Poll showed that 50 percent approved legalization and 48 percent disapproved -- Giuliani said the president might pay politically for his comments in swing states.

"The country's even, but the real issue is where is the country in the 10 states to decide this election," said Giuliani. "He's going to go to California tonight. Big hero with the Hollywood crowd doing this. Doesn't matter. He's going to win California. Texas, gonna be against it. Doesn't matter. However, how does it play in Ohio? How does it play in Wisconsin? How does it play in North Carolina? How does it play in Virginia? It plays against him."

Above, watch Rudy Giuliani talk about what factor same-sex marriage will have on the 2012 election