Former New York City Mayor Rudy Giuliani said today that he might run for president after all, but only if the Republican Party is “truly desperate,” which, he said, “maybe we are.”

“I would like to see somebody that emerges that I think would be a strong candidate for the Republican Party for president. If somebody does emerge that I believe can win, then I would probably support that person,” Giuliani said today at the National Press Club. “If I think that we are truly desperate, then I may run.”

“Which is the way I got elected mayor of New York City,” Giuliani said.  ”You know what my slogan as? ‘We can’t do any worse.’”

Giuliani, who made an unsuccessful bid for the Republican presidential nomination in 2008, said if he were to run, he “would have a chance of winning the presidency, a chance.” But the former mayor admitted he would have a hard time clinching the Republican nomination in 2012 because of how socially conservative the early primary states are and how vital they are to winning the nomination.

He said his previous presidential campaign made the mistake of focusing too much energy on winning nationally and not nearly enough on early primary and caucus states.

“Winning national polls doesn’t mean anything,” he said, giving advice to the current GOP presidential contenders. “Winning Iowa means something. Winning New Hampshire means something.  Winning South Carolina means something.

“And those primaries are tilted very much, at least two out of the three, are tilted very much in favor of conservative Republicans who are very strongly conservative on social issues,” he said. “I am simply not that conservative on social issues and I’m not willing to change just to become president.”

Giuliani, who was mayor of New York City during the Sept. 11, 2001 terrorist attacks,  said he would not make a decision about running for president until after the 10 th anniversary of the attacks, which is Sunday.

“I decided to put it off about two weeks ago as it got closer to Sept. 11. I didn’t feel it was right to answer questions like that then,” he said.

Giuliani had kind words for one of the current GOP presidential contenders, front-runner Rick Perry, whom he said he could see himself endorsing. Giuliani said he would not make any endorsements until the candidates have had a chance to firm up their positions on the economy and other issues in more GOP debates, such as the one scheduled Wednesday night.

“I do have a lot of admiration for Rick, [I am a] very strong supporter of his, a friend of his,” Giuliani said. “His record in Texas is exactly the kind of record we need in the United States, but I’m not sure he is the right candidate.”

Giuliani said if the election took place today, President Obama would lose to any of the top two or three GOP candidates because of the poor economy. He said the president’s jobs speech Thursday night is “his last chance to be moderate” enough to win re-election.

“If he remains tied to extremely unrealistic ideas about our economy and those unrealistic ideas are borne out by the poor performance of our economy, then it doesn’t matter if someone is right-wing, middle-wing or no-wing, they are going to beat him,” Giuliani said.