Window might be closing for a Joe Biden presidential run. Here’s why.

Weeks, even months of mixed signals from Vice President Joe Biden about his presidential intentions are increasingly testing the patience of Democrats who have otherwise been sympathetic to his family concerns, and the window of opportunity for him to emerge as a desired alternative to Hillary Rodham Clinton’s candidacy appears to be shrinking.

Since resuming work in late summer after the death in May of his eldest son, Beau, the vice president has alternately stoked speculation that he might join the Democratic field and said he lacked what he called the emotional fuel to do so.

But factors beyond his control are intruding on Biden’s deliberations. Outside ruminations on his tragic personal history have had the inadvertent effect of giving his grief an off-putting veneer of opportunism. On Thursday, a person close to the vice president said Biden was hoping that a group backing him would not air a widely publicized ad that refers to his family tragedy.

The group, Draft Biden, subsequently announced it would not air the ad.

At the same time, the White House has been deferential but has increasingly hinted that it is ready to move on. And talk of a Clinton campaign collapse has eased as her standing in the polls has stabilized before the first Democratic debate Tuesday.

One longtime Biden associate, who months ago thought the vice president could afford to sit out some of the first nominating contests if needed, said he has become less sure.

“I don’t know,” he said, echoing others close to the vice president who would not be named discussing private conversations but also expressed new doubt that he’ll ultimately join the race. “If she collapses, he can. I’m not so sure she’s going to collapse.”

Logistically, time is running short as well. In Iowa, which casts the first nominating ballots of 2016, one prominent Democrat suggested that Biden’s opportunity to seriously compete in the state is rapidly dwindling. He calculated that it would be late November before a fully staffed Biden campaign could be running there, leaving less than 90 organizing days before the February caucuses.

“That’s a very tall order,” the strategist said, “one that looks almost insurmountable at this point.”

The vice president’s office has stopped commenting for the record on reports of an imminent announcement. But close aides insisted he hasn’t made a final decision. They say that the question of whether he and his family are ready to endure the rigor of a campaign so soon after Beau’s death has not been answered conclusively enough to push ahead.

The vice president has spent almost every weekend since May close to his family in Delaware, where the subject of a campaign is likely to have been a recurring topic of discussion, according to a source close to the discussions.

As the first of many state filing deadlines approaches – Alabama’s is less than a month away – Biden has acknowledged that he “may not get there in time to make it feasible to be able to run and succeed,” as he told a Catholic magazine recently.

October brings three signposts: the debate, which Biden probably will skip; Clinton’s testimony before a congressional panel investigating the 2012 attacks in Benghazi, Libya, which has become a rallying point for her campaign; and a key Iowa Democratic Party dinner on Oct. 24.

Iowa has no filing deadline; on caucus night, more than 1,600 precinct-level meetings are held across the state, and winning requires an intensive organizational effort to persuade supporters to turn out in the winter cold and sit through a series of speeches before they can vote.

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“You don’t have to be a genius to organize in Iowa, but you need to hire people with experience,” said the veteran party strategist, who asked to remain anonymous to avoid antagonizing Biden or his supporters. “Identifying them and getting those who aren’t already committed to a campaign takes time.”

Former Pennsylvania Gov. Ed Rendell, a Clinton supporter, said Biden could still decide on a run as late as mid-November, though he doubted he would run.

He said he didn’t think there was a limit to Democrats’ patience – “He’s got a lot of chits with all of us” – but noted that after weeks of being included in polls, Biden still trails Clinton and in some cases Sen. Bernie Sanders in key states.

“With all the goodwill that Joe has, for him to still be where he is in the polls – it’s pretty daunting,” he said.

And from the White House come indications of an administration itching to refocus on its remaining time in office. At a news conference last week, President Obama referred to “if and when” Clinton is president, and on Tuesday, Press Secretary Josh Earnest noted that Clinton is “the leading candidate” for the nomination, even as he later said Biden should take what time he needs.

Alternatively, though, Biden has dropped hints in recent months that a third presidential bid might be in the offing and even sketched out a campaign message as a warrior for the middle class.

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On Thursday, Biden spoke at a Washington conference on job creation and infrastructure immediately after Sen. Elizabeth Warren, a favorite of the progressive base with whom he met privately in August, stoking talk of a possible dream ticket of Democratic luminaries.

Biden heaped praise on Warren, a Massachusetts Democrat, as “one of the most articulate people in the United States Congress,” before delving into a speech on the critical need for investment in infrastructure to aid the middle class. He insisted that the economic stimulus, whose implementation he oversaw, was “the most competently run program in the history of the United States for the amount of money involved.”

Last weekend, Biden and Clinton spoke at separate Human Rights Campaign events, a rare instance of the two courting the same key Democratic constituency in close proximity. And Tuesday, as he addressed labor leaders at a White House summit, Biden’s call to action seemed to include a direct swipe at his would-be rival’s former job as President Obama’s top diplomat.

“We need your muscle, we need to move. If I don’t move, I’ll be demoted to secretary of State or something,” Biden said, before pointing to the assembled press corps to stress: “That’s a joke!”

Without a definitive signal from Biden, though, the independent effort promoting his candidacy has ramped up -- sometimes in ways that don’t conform to his wishes.

The clearest example involved the new ad that the Draft Biden super PAC released on Tuesday urging him to enter the race.

The dramatic 90-second ad opens with Biden’s own words, addressing a gathering weeks before his son died of cancer, reflecting on another personal tragedy: the car accident in 1972 that killed his first wife and infant daughter and left his two sons seriously injured, just after Biden’s election to the Senate.

“By focusing on my sons, I found my redemption,” Biden is heard saying, as a montage of black-and-white photos of him and his family plays.

The ad has not aired on paid television spots, although portions of it have appeared on cable news shows. Thursday, Biden made clear that he did not want it to air.

“The vice president appreciates that they are trying to help,” the person close to Biden said, speaking on condition of anonymity to discuss his deliberations. “But he has seen the ad and thinks the ad treads on sacred ground and hopes they don’t run it.”

The outpouring of sympathy for Biden after Beau’s death, and the admiration of many for the way he has conducted himself publicly since, has certainly enhanced the vice president’s public image in a way that would serve his campaign.

But just a day before the Draft Biden ad launched, Politico reported that it was Biden himself who told a New York Times columnist months earlier that his son’s dying wish was for him to run. The report cast the revelation as evidence of political calculation by Biden, a characterization the vice president’s office called “offensive.”

“The bottom line on the Politico story,” the vice president’s office said in a statement, “is that it is categorically false.”

Times staff writer Mark Z. Barabak contributed to this report.

For more White House coverage, follow @mikememoli

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