Former Democratic vice presidential nominee John Edwards said Sunday he would have to "seriously" consider another shot at the job if asked by White House hopeful Barack Obama.

But the former North Carolina senator, who unsuccessfully ran for the party’s nomination this year and was on John Kerry’s ticket in 2004, reaffirmed that he was not actively seeking to be Obama’s running mate.

Two prominent Republicans also denied they were in the hunt to be the VP candidate of Senator John McCain, Obama’s opponent in the November election.

Edwards told ABC News: "I’d take anything he asks me to think about seriously, but obviously this is something that I’ve done and it’s not a job I’m seeking."

The comments of the anti-poverty crusader appeared to leave open some wiggle room, after he had told Spanish newspaper Vanguardia earlier this month that "the vice presidency is not a position that I desire."

Obama has been stepping up a discreet search for a running mate, although the process has been hampered by the departure of his chief vetter, Jim Johnson, in a controversy over favorable mortgage terms.

Others tipped for the Democratic VP job include senators Joseph Biden and Jim Webb, along with Kansas Governor Kathleen Sebelius and Pennsylvania Governor Ed Rendell.

Obama’s primary foe, Hillary Clinton, says she is not in the running.

Louisiana Governor Bobby Jindal, the 37-year-old son of Indian immigrants, said media speculation touting him as a potential running mate for McCain was "flattering."

"The reality is, I’ve got the job that I want," the Republican rising star told CBS News. "We’ve got the chance to make once-in-a-lifetime changes and reforms in our state. I want to be a part of turning Louisiana around."

Other names in the Republican frame include former Massachusetts governor Mitt Romney, who dropped out of the Republican White House race in February, Florida Governor Charlie Crist, and Minnesota Governor Tim Pawlenty.

Obama spent a rare day with his family in Chicago, and addressed parishioners in the largely African-American Apostolic Church of God to demand greater responsibility from absentee fathers.

In a Father’s Day speech at the church, Obama also pressed for government action to help struggling parents, through tax breaks, job training and family-friendly employment laws.

The African-American Illinois senator amplified one of his campaign themes in condemning missing fathers who have "abandoned their responsibilities, acting like boys instead of men."

"You and I know how true this is in the African-American community," Obama said, recapping government statistics showing more than half of all black children live in single-parent households.

Such children are five times more likely to live in poverty and commit crime, nine times more likely to drop out of school, and 20 times more likely to end up in prison, he said.

"And the foundations of our community are weaker because of it," said Obama, who dwelt on his own challenges growing up with a single mother from the age of two after his Kenyan father abandoned them.

In the week ahead, Obama and McCain are likely to rejoin battle over the economy as Americans reel from home foreclosures, rising gasoline prices and job losses.

John Boehner, the minority leader in the Democratic-controlled House of Representatives, acknowledged on CNN that Republicans have "a steep hill to climb" this election year.

But his party’s tax-cutting platform was "a much better prescription than what Barack Obama and the liberal Democrats want, which is higher taxes, bigger government in Washington and more control from Washington," Boehner said.

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