Washington (CNN) For Joe Biden, it's about more than Beau.

Biden would likely have jumped into the Democratic primary months ago if his beloved elder son's dying wish that he mount another White House run was the only factor in his political deliberations.

Biden, though, also has a list of deeply political and practical obstacles to resolve before deciding on a bid, which already looks like an uphill battle against declared Democratic candidates Hillary Clinton and Bernie Sanders. A source close to the vice president said there will be a "family conversation" this weekend to discuss his candidacy.

Biden must consider whether his late entry in the race would leave him too far behind in fundraising and organization to mount a campaign, then identify a genuine lane of support that could guide him toward the nomination -- and also ponder whether Democrats would be angered if he weakens Clinton, who many in the party still see, despite her troubled campaign, as the most likely nominee and potentially the first woman president.

And then there is perhaps the most fundamental question -- is his grief-stricken family really up to the trials of a presidential campaign?

But those considerations were overshadowed by a Washington frenzy Tuesday over a news report suggesting that Biden personally leaked his son's desire to see him make a third bid for the White House to New York Times columnist Maureen Dowd.

The report, in Politico, raised the question of whether Biden was using the death-bed plea for political advantage.

But David Axelrod, a senior CNN political analyst who knows Biden well from working with him in the Obama White House, said such a notion was off-base.

"I just don't buy into the interpretation that he would try and essentially politicize what was one of the most horrific events of his life," Axelrod said.

Biden's office issued a vehement dismissal of the story.

"The bottom line on the Politico story is that it is categorically false and the characterization is offensive," said a Biden official on condition of anonymity.

Vice president known for spilling his heart

Such is the affection in which Biden is held, and the protective feelings that he fostered after his deep personal loss, that few Democrats were willing to talk openly about the Politico story or to debate whether Biden was exploiting his grief for political gain.

Some did acknowledge that the issue of his son's passing had indeed become closely wrapped up in the decision-making process of his run -- and that his public comments on it have become political simply by the very nature of his position.

But Biden is notorious for loquacity, and it would not be unusual for him to be spilling his heart out to a prominent figure -- especially one he has known for years, such as Dowd, even if he was not trying to make a political point.

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Indeed, The Wall Street Journal had the first reports that Beau Biden had issued an emotional plea for his father to run against the Clinton machine. The newspaper report was in late June, just a month after Beau Biden's death, though the information did not appear to come from the vice president himself.

But while Biden's public agony over his son's death is clearly genuine, the inspiring -- and public -- way in which he has processed his grief has helped to redefine his public image in a way that could be an asset in a presidential campaign.

No longer -- or at least until he enters the unforgiving environment on the campaign trail -- is Biden primarily seen as a kind of garrulous, gaffe-prone uncle known for windy rhetoric.

Instead, he now seems more like a dignified elder statesman who has conquered life's toughest blows and is still standing.

He reached that point through a genuine outpouring of grief, appearing broken by his loss at events soon after Beau's death, sympathetically pouring out his feelings on Stephen Colbert's couch and then stoking new speculation about his political future with a Labor Day stemwinder speech in Pittsburgh.

In fact, Biden offered Americans a window into his soul, and a lesson in dignity that impressed people on both sides of the nation's harsh political divides.

Would Biden's recent posture help him with voters?

One result of Biden's emotional trials over the last few months is to remind Americans of the way tragedy has stalked his life -- his wife and infant daughter died in a car crash shortly after he was elected to the Senate in 1972 -- and his fortitude in overcoming deep personal misfortune. It has given him the kind of authentic appeal that many politicians -- like Clinton, for example -- spend years trying to convey.

But if Biden was indeed trying to score political points by talking about his son's death, it would be unlikely to represent a sound bet.

James Campbell, a nationwide election forecaster from the University at Buffalo, New York, said that while Biden's public grieving might make voters more sympathetic toward him, it would be unlikely to remold the political logic that decides elections.

"I think it plays to his strengths already, in that he is a fairly empathetic figure and he seems very likeable. The tragedy he has gone through only highlights that," he said. "But it will be a very short run. While people will obviously be very sympathetic to him because of it, I don't imagine many people's votes will change because of it."

The idea, furthermore, that in his son's death Biden found a reason to run for president also tests credulity. He has, after all, mounted two short-lived and unsuccessful runs for the White House in the past and has made no secret that he would love the top job.

Friends have said that Biden believes that he is uniquely qualified to serve as president at this time, after two terms as vice president and after piling up years of foreign policy experience in the Senate.

Photos: Photos: Vice President Joe Biden Photos: Photos: Vice President Joe Biden U.S. Vice President Joe Biden began his career in politics in 1972, winning election to the Senate at the age of 29 (he was 30 when he took office). The Delaware Democrat was reelected to the Senate six times, including 2008, before becoming the 47th vice president of the United States. Hide Caption 1 of 14 Photos: Photos: Vice President Joe Biden Biden is sworn in for his second term as vice president by Supreme Court Justice Sonia Sotomayor, with his wife, Jill, and son, Beau, by his side, on January 21, 2013, in Washington. Hide Caption 2 of 14 Photos: Photos: Vice President Joe Biden Biden presides over a ceremony in Baghdad to formally mark the end of the U.S. combat mission in Iraq on September 1, 2010. Hide Caption 3 of 14 Photos: Photos: Vice President Joe Biden Biden and President-elect Barack Obama wave to the crowd at their election night party at Grant Park in Chicago on November 4, 2008. Hide Caption 4 of 14 Photos: Photos: Vice President Joe Biden Biden speaks after being introduced as Obama's running mate while campaigning together after the Democratic National Convention in 2008. Hide Caption 5 of 14 Photos: Photos: Vice President Joe Biden From left, former Sen. John Edwards, Biden, Obama and Sen. Hillary Clinton at a debate of Democratic presidential candidates on April 26, 2007, in Orangeburg, South Carolina. Hide Caption 6 of 14 Photos: Photos: Vice President Joe Biden Biden releases his memoir, "Promises to Keep: On Life and Politics," in 2007. Hide Caption 7 of 14 Photos: Photos: Vice President Joe Biden As a ranking member of the Senate Foreign Relations Committee, Biden is interviewed on NBC's "Meet the Press," concerning the war in Iraq on August 14, 2005. Hide Caption 8 of 14 Photos: Photos: Vice President Joe Biden While chairman of the Senate Foreign Relations Committee, Biden meets Afghan students during a visit to Kabul in 2002. Hide Caption 9 of 14 Photos: Photos: Vice President Joe Biden Biden is welcomed back after undergoing surgery for an aneurysm in 1988. Hide Caption 10 of 14 Photos: Photos: Vice President Joe Biden Biden announces his candidacy for the Democratic presidential nomination in 1988. After three months he drops out, following reports of plagiarism and false claims about his academic record. Hide Caption 11 of 14 Photos: Photos: Vice President Joe Biden While on the Senate Judiciary Committee, Biden meets with Sen. Frank Church, center, and Egyptian President Anwar Sadat after the signing of the Egyptian-Israeli Peace Treaty in 1979. Hide Caption 12 of 14 Photos: Photos: Vice President Joe Biden President Jimmy Carter and Biden attend a reception for the Delaware Democratic Party in 1978. Biden was the first senator to endorse Carter's presidential candidacy two years earlier. Hide Caption 13 of 14 Photos: Photos: Vice President Joe Biden At a convention in 1972, Biden and his first wife, Neilia, and his two sons take a photo with Delaware Gov.-elect Sherman W. Tribbitt and his wife Jeanne. Neilia Biden died in a car accident a few months later, after his first election to the Senate, along with their infant daughter, Naomi. Hide Caption 14 of 14

But should Biden jump into the race, any lingering warm feelings toward him would be tested by the reality of election politics -- his background, record, political reversals and failures, and family and associates' business dealings would all be fair game.

"He has been around politics for long enough to know that people are always kinder before you set foot on the battlefield than afterwards," said Axelrod. "People who said they are right behind you are suddenly a good distance back."

Another consideration weighing against a Biden run are the challenging politics. Though he is not yet in the race, rumors of his possible candidacy have been circulating for months. Biden trails Clinton in most national polls by 20 points and lags behind Vermont Sen. Bernie Sanders, who is making an unexpectedly strong run on the left of the party.

It remains unclear whether the vice president has a sufficient avenue of support that could propel his candidacy through the early primary races. His experience in 2008, when he won less than 1% in the Iowa caucuses, could be an ill omen.

Biden run would have a big ripple effect

Biden must also satisfactorily answer another big question: Is there sufficient support from Democratic donors to bankroll a frenzied three-month effort to build a political operation in early-voting states?

If he does get in the race, Biden could conceivably pull votes from Sanders Democrats who are supporting the Vermont socialist just because of antipathy to the former secretary of state. But there is much more evidence from polling to suggest that he would draw support from Clinton -- with whom he served in the Obama Cabinet and appears to have few substantive policy differences.

He may additionally be considering the impact on his political legacy in a party in which Clinton is viewed as having a genuine chance to make history as the first female president.

And one of the central, but unspoken, rationales of a Biden campaign would be the idea that he would be ideally positioned should Clinton's problems over a controversy concerning a personal email server lead to legal issues that cripple her campaign.

Any suggestion that that is his real motivation, though, could alienate key sectors of the party.

"You don't run for president hoping somebody goes down," said Brent Budowsky, a veteran Democatic operative and newspaper columnist. "Women that support Hillary will be enraged at a vulture candidacy by Joe Biden."