Standing beside President Obama and his wife, Jill, Vice President Biden announced he would not be a candidate for president in 2016 but also would "not be silent" about what he feels the nation needs. (AP)

Vice President Biden’s announcement Wednesday that he will not seek the 2016 Democratic presidential nomination has given a further boost to resurgent front-runner Hillary Rodham Clinton and clarified her terms of engagement with Bernie Sanders, who is waging a challenge from her left.

Biden ended months of speculation with his blunt acknowledgment that “the window on mounting a realistic campaign for president” has closed for him, as he and his distraught family have worked through their grief over the death in May of his eldest son, Beau.

“Unfortunately, I believe we are out of time — the time necessary to mount a campaign for the nomination,” Biden said as President Obama stood by his side in the White House Rose Garden.

Polls indicate that, had Biden jumped in at this late stage, he would have drawn votes primarily from Clinton. The two come from the same center-left sector of the Democratic Party, have similar long-standing institutional ties and allegiances within the party, and can both claim relevant national security and legislative experience.

The massive interest surrounding Biden’s deliberations had underscored Clinton’s significant vulnerabilities, as well as her strengths, in her quest for the nomination and in a general election contest.

But the former secretary of state also has a formidable — probably insurmountable — head start. And after a bumpy few months, her standing has improved considerably over the past week, after her commanding performance at the first Democratic debate in Las Vegas.

“She was the likely nominee yesterday, and she’s the slightly more likely nominee today,” said David Axelrod, who was the chief political strategist for Obama’s two presidential campaigns, including his 2008 primary victory over Clinton.

With Biden’s decision, the Democratic primary has become a two-way race between Clinton and Sanders, a senator from Vermont who describes himself as a democratic socialist. Sanders has been drawing massive crowds of exuberant supporters across the nation, and he nearly matched Clinton’s fundraising in the most recent quarter.

“In some ways, it’s simpler now,” said Sanders adviser Tad Devine. “It’s Bernie. It’s Hillary. It’s binary. It’s not triangular anymore. Choose one or the other.”

Meanwhile, two more tests loom before Clinton in the coming days.

The first is her long-
anticipated testimony Thursday before the House Select Committee on Benghazi, which is investigating the 2012 attacks in Libya that left four Americans dead, including the U.S. ambassador. And on Saturday, she and the other Democratic contenders will speak at a high-profile Democratic dinner in Iowa, which is closely watched as an early gauge of organization and message in the state that will hold the first contest of the primary season.

Vice President Biden announced that he is not running for president. The Fix’s Chris Cillizza explains why this is important for rival Hillary Clinton and the Democratic Party. (Alice Li/The Washington Post)

While Biden’s decision was undoubtedly good news for Clinton, Axelrod said that it also may encourage some of her more insular tendencies. Those reflexes have fueled the controversy over her use of a private e-mail system, rather than a government one, while she was secretary of state.

“The absence of Biden and the intrigue poses a different challenge for her. She never handles prosperity well,” Axelrod said. “What she shouldn’t do is retreat into a zone of comfort here, of reticence and caution.”

In the months leading up to the first debate, Clinton’s poll numbers had sagged under the weight of the e-mail controversy, which had deepened public misgivings about her character, and the growing support for Sanders.

Lately, she has moved to the left on several issues important to the Democratic base, including trade, and given more interviews to the national media.

Her campaign has been displaying its muscle on the ground — which includes dozens of campaign offices in the early states and a staff many times larger than any other candidate.

Meanwhile, Biden’s deliberations loomed over the campaign. It had become increasingly clear that he wanted to be president — a goal since he came to the Senate in the early 1970s and that he sought twice unsuccessfully. The question, for him and his family, was whether it was achievable and whether they had the emotional stamina for it in the wake of Beau Biden’s death.

Biden pointed to the impact of grief on his presidential plans. “I know from previous experience that there’s no timetable for this process,” he said. “The process doesn’t respect or much care about things like filing deadlines or debates and primaries and caucuses.”

In a wide-ranging speech that could have been the announcement address he would never deliver, Biden encouraged Democrats to run next year on Obama’s record. Biden touched on policy goals and priorities he intends to tackle in the home stretch of the president’s second term: issues such as fighting the influence of money in politics, as well as finding a cure for cancer.

“While I will not be a candidate, I will not be silent,” he said. “I intend to speak out clearly and forcefully, to influence as much as I can where we stand as a party and where we need to go as a nation.”

Although Biden is widely popular among Democrats, polls show that he would have entered the contest as a significant underdog. In a Washington Post-ABC News poll released Tuesday, 16 percent of Democratic-leaning voters said they would support him for the nomination, putting him in third place behind Clinton at 54 percent and Sanders at 23 percent.

Recent days have brought reminders of the obstacles he would have confronted had his candidacy moved from the theoretical stage.

Although his freewheeling, undisciplined style of speaking has been part of his charm, for instance, it has also gotten him into trouble — as it did on Tuesday, when he appeared to revise a long-standing account of where he had stood on the 2011 raid that killed Osama bin Laden. In the past, Biden had said he opposed it; this time, he recalled telling Obama that he favored sending a team of Navy SEALs into Pakistan to kill or capture the al-Qaeda leader.

In an actual presidential campaign, the reaction to that kind of inconsistency would have been brutal.

After his announcement, Clinton telephoned Biden, and she issued a statement saying he is “a good man and a great Vice President.”

“I am confident that history isn’t finished with Joe Biden,” she added.

Sanders put out his own statement, in which he thanked Biden “for a lifetime of public service and for all that he has done for our nation.”

Anne Gearan and John Wagner contributed to this report.