WASHINGTON — (CNN) Joe Biden faces a host of complicated questions in deciding whether to run for president. But in the end, his decision could rest on a very simple one.

As he mulls one last bid for the White House, Biden is working through an MRI of the soul, filtering his undimmed dreams of the presidency and gnawing grief for his son Beau, who before he died reportedly urged him to run.

He must ask whether his age — he would be 74 when he took office — would permit a long, grueling campaign, not to mention a subsequent presidency, and ponder the strains of a race on his family, which has endured more pain than most could bear.

But even if he conquers those concerns — and can shed an image of sometimes being a gaffe machine — Biden has to ponder something more basic: Where can he beat Hillary Clinton?

The more Biden’s potential primary prospects are examined in detail, the narrower they seem to become.

Clinton might be battered by a rough start to her campaign, haunted by the controversy over her emails, criticized for having a political tin ear and surprised by the surge of left-wing opponent Bernie Sanders. But she remains a formidable front-runner for the Democratic nomination.

So great are her advantages that many Democrats privately agree that Biden could only triumph if so-far unknown revelations about her use of a private server as secretary of state — currently being investigated by the Justice Department and the FBI — cause her campaign to implode.

“There really isn’t a lane (for Biden) unless Hillary Clinton has legal difficulties in relation to her email situation,” said Neil Levesque, executive director of the New Hampshire Institute for Politics at Saint Anselm College.

Clinton fans appear to have plenty to worry about: Recent polls show rising unfavorability ratings that seem to counter claims by her campaign that voters don’t really care about the episode. And Quinnipiac University polls last week had Biden doing better than Clinton in a hypothetical general election matchup against GOP candidates, including Donald Trump, in swing states Florida, Ohio and Pennsylvania.

But Biden backers don’t just rely on Clinton liabilities to make a positive case for why he’s the best choice to succeed President Barack Obama, who CNN reported on Monday has given his blessing for a campaign by his vice president.

“Joe Biden is arguably the most consequential vice president in history. His fingerprints have been on pretty much every foreign policy and domestic issue,” said Steve Schale, a key Obama campaign aide who has signed up with the “Draft Biden” effort, on CNN Tuesday.

But though he’s beloved by Democrats, radiates a love for campaigning that Clinton can’t match and has stood shoulder-to-shoulder with his boss during the most sweeping progressive presidency in decades, Biden still faces unpromising political math.

Democrats in early voting states, political analysts and consultants all suggest that if Biden does have a path to the Democratic nomination, it is exceedingly slim.

“I think he would be fighting for a lot of the same voters that have been canvassed by Hillary Clinton and are firmly in her camp,” said Michael Bronstein, a Pennsylvania-based political consultant, who is not working for any presidential candidate.

“He is starting off fairly late in the cycle. A lot of the top-level support that you have to have being an institutional candidate like the VP certainly has been locked up,” said Bronstein. “It’s very hard to see where the light of day is in the Democratic establishment to bring another candidate into this space.”

Biden’s biggest liability might be the fact that he lags far behind in the critical task of building the precinct-by-precinct network needed to identify voters and get them to the polls in early caucus and primary states.

He also starts off well behind Clinton in a duel over key Democratic constituencies, like African-Americans and women, who strongly back the former first lady but whom the vice president would need for a successful campaign.

Biden might also struggle to tap a rich Democratic donor base already lined up by Clinton, and any hope of running a populist crusade to the left of the former first lady is complicated by the strength of Sanders.

A Biden campaign would seek to leverage the candidate’s undeniable connection to blue-collar voters and his fabled tales of a hard-scrabble upbringing in Scranton, Pennsylvania — and to subtly play on suspicions of the wealth Clinton now enjoys.

“If you look at the way Democrats have struggled with working-class white voters primarily, I think Joe Biden is a guy that has come from that world. He was a middle-class guy growing up, and he has never lost his roots,” said Schale. “He gives us a chance to talk to some voters that we have struggled with in the last few cycles.”

But it is not yet clear that Clinton’s own ties with this key voting bloc have eroded. In fact, blue-collar Americans in Rust Belt states like Pennsylvania and Ohio helped her prolong her 2008 campaign against Obama for months. Back then, she profited from ties first forged in Bill Clinton’s 1992 campaign and a presidency remembered for middle-class prosperity.

She’s working hard now to build a campaign based on restoring what she calls the basic bargain of America: that if you work hard, you should get ahead.

Another potential Biden approach is to argue that having spent seven years a heartbeat away from the presidency, he is uniquely prepared to be commander-in-chief.

But Clinton has her own experience to tout — after all, she served four years as secretary of state and can relate to Obama supporters how she swallowed her defeat in 2008 to join the President’s team-of-rivals Cabinet.

In the end, though, presidential primary races boil down to amassing delegates, winning state races and methodical organization. And here again, Biden is at a disadvantage, especially in the early voting states that could dictate the shape of the race.

He failed to win even 1% of the vote in the Iowa caucuses in 2008 and was overshadowed by Obama, John Edwards and Clinton.

He might do better this time — thanks to his enhanced reputation as vice president — but he has a lot of work to do.

In a CNN/ORC International Poll of the Hawkeye state this month, the vice president was at 11%, behind Clinton at 54% and Sanders at 31%.

Clinton has learned the lessons of her 2008 defeat in Iowa by quietly building a broad political network there. So with only five months to go before the 2016 caucuses, and with campaign funds possibly at a premium, could Biden emulate Clinton?

“If you scramble, you could get it done, I suppose, but to pull that off you really have a challenge,” said Jerry Tormey, a senior Iowa Democratic Party official. “I think there would be a lot of people who would stand by their commitment and stay with Hillary. It would be a challenge for Joe.”

If not Iowa, then why not New Hampshire, where Clinton is under pressure from Sanders, whom she trailed in one recent bombshell poll?

Again, Biden is starting well behind. Clinton has already snapped up legions of volunteers and party elites, building on long political relationships in the state, which she won in 2008, just as her husband did in his first presidential race.

“The Clinton campaign has locked up not only what they had way back in ’92, they have locked up the Obama people, too,” said Levesque.

Edward Shumaker, a former U.S. ambassador to Trinidad and a supporter of both Clintons who also worked on Biden’s short-lived 1988 presidential campaign, said the vice president’s late start would be a serious disadvantage in the Granite State.

“It’s certainly not impossible but — to use a sports metaphor from diving — the degree of difficulty would be quite significant,” he said.

So, South Carolina, which follows New Hampshire in the nominating race, could shape up as make-or-break for Biden. Here there may be some good news for him.

Sources in the state say Biden enjoys significant support among activists, county chairs and local party officials and would enjoy a near-level playing field with Clinton.

He would get a break because Sanders is expected to be less strong in South Carolina than in Iowa and New Hampshire — given that his coalition of white progressives is less prevalent in the Palmetto state and he hasn’t registered much support from black voters.

But Biden would still be starting from behind.

“Can Biden compare to Hillary’s outreach to African-Americans?” asked Scott Huffmon, professor of political science at Winthrop University, South Carolina.

“African-Americans are the absolute must-haves of the South Carolina Democratic Primary,” he said, referring to a voting bloc that made up 56% of the party primary electorate in 2008.

Both Bill and Hillary Clinton have worked exhaustively to repair ties with African-American voters since the bitter 2008 primary clash in South Carolina that was won by Obama after a remark by the former president was perceived by some to have racist overtones.

They have been so successful that in a CNN/ORC Poll in August, 49% of Democratic voters said the former first lady would do the best job in tackling race relations, well ahead of Sanders or Biden.

An endorsement from Obama could be decisive in the state, but the President is thought unlikely to intervene directly in a contest between two such close allies as his vice president and former secretary of state.

The next contest of the early nominating season, in Nevada, also looks dicey for Biden given Clinton’s historic popularity among Hispanic voters.

Though the vice president could argue that he played a key role in Obama’s decision to stay the deportations of millions of undocumented migrants through executive action, the Western desert state looks just as likely to underline the challenging questions that could dog his yet-to-be-launched primary campaign.

Still, despite the daunting obstacles for a run, there appear to be growing signs that Biden is seriously contemplating entering the race, perhaps simply to position himself in case Clinton stumbles. Presidential politics is always unpredictable and the only certainty is that no one can win the presidency without entering the fray.

“You never know what is going to happen until somebody gets into the race,” said Bronstein. “Presidential politics is messy.”

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