Former Mayor and Gov. Ed Rendell - who said that he has not talked with Nutter on this issue - said he thinks that Nutter could have a shot in D.C. under Obama, if he wants one.
"I think the mayor would be on their radar screen, and I think the mayor could fill a number of Cabinet positions or sub-Cabinet positions," Rendell said. "I'm not sure the mayor would want to. . . . I think he could expect an offer."
Nutter has been careful to tamp down speculation. In a statement, he said that he was not going to play the "speculation game" and said that he could do more to help the president by "staying mayor of Philadelphia and doing my job through the end of my term."
But when asked in person if he would pledge to stay mayor for his full four-year term, which runs through 2015, Nutter declined, saying, "I gave you the answer. It's the only answer."
Nutter's national profile has skyrocketed in recent years. He serves as president of the nonpartisan U.S. Conference of Mayors and is a frequent guest on cable news shows and Sunday talk programs.
Some think that his rising national fame, combined with an increasingly tough road at home, might make a new job attractive. In Philly, Nutter faces a limited budget, combative unions and a restless public - and the further he goes into his second term, the more his political power wanes as interest turns to the 2015 mayoral election.
"If there were political jobs that seemed natural and on the horizon in Pennsylvania, it might be a different story," said Zack Stalberg, president of the Committee of Seventy and former Daily News editor.
Were Nutter to leave office early, the keys to the city would go to City Council President Darrell Clarke, at least temporarily. But, after some time in Washington, Nutter could be better positioned for a statewide run for office, or to take on a national job.
"He could have an elective career afterwards if there are any vacancies," said Oxman. "It's why I have said to people in a very serious way, the next mayor of Philadelphia is Darrell Clarke."
Clarke declined to comment.
Experts said that getting a job with the president doesn't typically start with a phone call from out of the blue from the Oval Office. Nutter would likely have to indicate his interest and there would likely be extensive negotiations.
Comcast Executive David L. Cohen said that there were lengthy talks regarding Rendell's appointment as chairman of the Democratic National Committee, a post he held in 2000 after he left office as mayor.
"There were back-channel conversations to me; there were back-channel conversations to other people," said Cohen, who served as chief of staff when Rendell was mayor. "For months before there were conversations between Clinton and Gore and Rendell; there were other conversations.
"The mayor would have to have an interest for this to go anywhere and I honestly have no idea."
Contact Catherine Lucey at firstname.lastname@example.org or 215-854-4172. Follow her on Twitter @PhillyClout. Read her blog at phillyclout.com.