Vice President Biden is still mulling over a possible 2016 White House bid — but after Hillary Clinton's polished performance in the first Democratic presidential debate, has the window of opportunity closed? The Fix's Chris Cillizza explains where Biden can go from here. (Julie Percha/The Washington Post)

Vice President Biden’s lengthy deliberations over whether to run for president hit a sizable speed bump this week. Hillary Rodham Clinton’s strong debate performance robbed Biden of a partial rationale for running and also probably shortened his timeline for making a decision.

The day after Tuesday’s debate, speculation among Democrats about Biden’s future was inextricably connected to Clinton’s dominant evening against Sen. Bernie Sanders (I-Vt.) and three other rivals. The question on the minds of many was whether there is now adequate space in the Democratic race for the vice president.

The path for Biden has always looked daunting, despite the desire among some Democrats for him to enter the race. He has trailed Clinton in all the polls, nationally and in Iowa and New Hampshire. He has been no better than competitive with Sanders, though their support overlaps less than his does with Clinton. Whatever his capacity to raise money, he would be starting from scratch.

After the debate, Clinton aides were not saying explicitly whether Biden has a path, but after weeks of neutral comments, the language turned. Clinton’s campaign chairman, John Podesta, told my colleague Philip Rucker that time is running short for Biden and made clear that if the vice president were to get into the race, he would face a formidable opponent in the former secretary of state.

Take a look at the issues discussed and exchanges between candidates.

“He needs to make up his mind,” Podesta said. “She put in a tremendous debate performance tonight, and I think that she occupied a space in the party that showed that she was going to fight for this nomination, take the fight to the Republicans, put forward a program that people could really grab onto, believe in, and she was going to fight for the people she’s been fighting for all her life. If he wants to get in and challenge her, then he needs to do that, and that’s his right.”

Others outside of Clinton’s orbit echoed that sentiment. David Axelrod, the chief strategist on President Obama’s campaigns, wrote for CNN Wednesday that Biden’s current standing in third place in national polls is unlikely to change following the debate — perhaps a reason to stay out.

“As a matter of pure politics, Clinton’s good night reduced the rationale for Biden’s candidacy,” Axelrod wrote. “After Tuesday, the calls on him to save the party from a weak front-runner will be more muted.”

For weeks, Biden’s decision-making process has been complicated by the absence of clarity on the two most important questions he has been trying to answer: his family’s emotional health and Clinton’s political vulnerability.

The first of these is highly personal and, by all indications, the more important. Biden has needed to be assured that he and his family are emotionally ready for a grueling campaign as they continue to mourn the loss of his son Beau at age 46 after a long battle with brain cancer.

Beau Biden’s death late last spring shattered the entire Biden family. Individually and collectively, they have been struggling to move forward. Those who know the vice president say some days are better than others for him, as they are for various other family members.

Biden has spoken publicly about this question several times in recent weeks. At no time was he able to give a definitive answer to the question of whether he and his family could give a full commitment to the demands of a campaign. In fact, he’s consistently suggested that he and they were not ready.

It was perhaps Biden’s hope that time would resolve this question, that as the weeks passed, he would feel more and more prepared to do what is necessary to run for the presidency and that his family would be able to carry on knowing he would often be an absent patriarch.

That process inevitably clashed with the practical realities of what a campaign requires — the recruitment of talent, the creation of an organization, the prodigious fundraising, the constant travel, the development of a rationale and message — and it has been obvious for weeks to those watching the vice president’s process of decision-making that there would likely be no real clarity by the time he had to decide.

The longer Biden has deliberated, the more the issue of Clinton’s vulnerability has come to the forefront. As questions about her use of a private e-mail server swirled, as her personal image deteriorated, as her perceived weaknesses grew, nervous Democrats looked to Biden as a possible backstop. Calls into his orbit gathered force, urging him to run.

But as with his family’s emotional readiness, there has never been real clarity on whether Clinton is truly damaged or temporarily weakened. Democrats tracking Biden’s deliberations have predicted that he would not know the answer to that question by the time he had to make a final decision. That’s all the more true after Tuesday’s debate.

Biden’s political advisers have spent weeks preparing for a campaign and have been persuaded that there is plenty of talent and enough money to launch a serious bid for the White House. But outside those circles, there has been a debate among Democrats about whether there is really a clear path for Biden to capture the nomination.

For all the concerns among Democrats about her, Clinton has remained the favorite for the nomination. After the debate, her stock among Democrats was on the rise. That’s because with all eyes on her and with the vice president absent from the stage, she delivered impressively.

She took nothing for granted and arrived exceedingly well prepared after a series of mock debates. She showed no hesitation to criticize Sanders, her leading rival. She showed grit when challenged and humor when it helped. Above all, she left no doubt about her determination to fight for the Democratic nomination and to lead her party against the Republicans in the general election.

The overnight reviews on Clinton were extremely positive, perhaps somewhat too positive as is sometimes the case with debates. There is a difference between turning in a good debate performance and fundamentally changing voters’ perceptions.

Anyone who doubts that should look back to Mitt Romney’s presentation in the first debate against President Obama in October 2012. Romney overwhelmed Obama that night and was judged the clear winner. But he was still saddled with questions about his candidacy and with the underlying forces in the campaign, which ultimately helped Obama prevail.

Sanders gave Clinton a gift when he batted away the issue of her e-mails. But that was only for the duration of the debate. An errant comment by House Majority Leader Kevin McCarthy has changed the calculus on her upcoming testimony before the House committee investigating her e-mails and the deaths of four Americans in Benghazi, Libya, in September 2012.

Clinton reassured nervous Democrats by reminding them of her talents as a debater. She did not fully alleviate her vulnerabilities. She remains hostage to new revelations and the drip, drip, drip that lies ahead on her e-mails, and it will take more time and more than one debate before anyone can say whether she is turning around perceptions of her on questions of trust and honesty. But that doesn’t offer Biden any help. Right now, she looks strong.

Biden has been a sympathetic figure through these weeks of deliberations, as a grieving father, as a working-class politician who speaks passionately for the middle class, as a politician equipped to serve as president. His circumstances have earned him the time to deliberate, but in recent days, the patience of those in his party has begun to wane.

Clinton long has said he should have the space to make whatever decision he thinks best. What she did on the debate stage Tuesday night sent another signal that he cannot ignore.