Vice President Biden presides over the Senate at the U.S. Capitol on Dec. 5. (Senate Television via AP)

Vice President Biden’s tribute tour reached a crescendo Wednesday in the rarest possible fashion: He barely said a word on the Senate floor.

Biden, who for 36 years filled the chamber with voluble oratory, sat in the presiding officer’s chair serving in his other capacity, president of the Senate, as a bipartisan collection of colleagues poured out tributes for the outgoing vice president. The senators mixed personal and professional stories, highlighting how often Biden overcame family tragedy and kept on serving, first in the Senate and then as vice president.

“That’s Joe Biden right there,” said Senate Majority Leader Mitch McConnell (R-Ky.), a key negotiating partner over the years. “Unbowed … unbroken … unable to stop talking.”

The chamber broke into laughter. Not actually a member of the Senate, Biden is forbidden from speaking aside from parliamentary rulings and issuing procedural orders. It was Biden’s third straight day in the Capitol, a victory lap that demonstrated his unique talent for brokering deals but also the empty feeling of never becoming president.

[After Senate tribute, Vice President Biden jokes about 2020 run.]

On Monday he oversaw the critical Senate vote that set up Wednesday’s final passage of the 21st Century Cures Act, a sprawling medical research bill that included $1.8 billion for the “cancer moonshot” that Biden plans to be the focus of his post-vice presidency.

It was a final partnership between Biden, who lost his son to brain cancer in May 2015, and McConnell, who overcame polio as a child and has a personal interest in regenerative medicine dealing with stem cell research. Their professional bond, usually focused on taxes and fiscal issues, culminated in a deeply personal mission for each politician.

Yet moments after that Monday vote, Biden couldn’t resist the presidential temptation in an exchange with reporters. “I’m going to run in 2020 . . . For president. What the hell, man,” Biden, 74, said.

By Wednesday evening, after dozens of speakers stretched his Senate tribute to 2½ hours, Biden headed to a reception in his honor and was more conclusive about his future. “I have no intention of running,” he told The Washington Post.

Monday’s comments about possibly running really just captured his personal disappointment in seeing Republican Donald Trump win this year’s White House race. In public and private, Biden had warned that Hillary Clinton’s campaign was not connecting with white working-class voters in key Rust Belt states, risking a Trump surge that might cost Clinton the race.

[Joe Biden wants Democrats to not give up on Trump voters]

At the request of Senate Democrats, Biden agreed to be their emissary into those key corners to try to connect with those voters, and the vice president relished that role, one last campaign to try to flip the Senate back to the Democrats. Instead, his worst political nightmare played out across almost every key state. Trump walloped Clinton among working-class voters, and the Democratic coalition that President Obama had built, particularly among minority voters, had uneven turnout in key cities.

He returned to the Capitol on Tuesday morning for a huddle with House Democrats, where some members encouraged him to become chairman of the Democratic National Committee — an offer he immediately rejected. Later Tuesday, he flew to New York to appear on Stephen Colbert’s “The Late Show,” wrapping up a journey that began with his September 2015 appearance on the CBS late-night show.

Then, just three months after his son’s death, Biden poured out his soul and made clear he wasn’t emotionally prepared to run a national campaign for president, yet the honesty struck a chord with a populace that craved authenticity from its politicians.

On Tuesday night, he told Colbert that his decision against running, made from the Rose Garden in late October 2015, left him disappointed but was the “the right decision for my family.”

“I don’t plan on running again,” he told the host. But, in his usual manner, Biden ended with a tease about 2020, saying he was in “better shape” than the president-elect: “Hell, Donald Trump’s going to be 74, I’m going to be 78.”

Shortly after the Senate approved the health bill Wednesday, Biden entered the chamber to oversee his own political tribute, arranged by Sen. Chris Coons (D-Del.), who holds Biden’s former Senate seat. Coons only reached the Senate because Beau Biden, then the Delaware attorney general, declined to run in 2010 for his father’s seat and charted a course that was supposed to end this fall with him winning the Delaware governor’s race.

Minority Leader Harry M. Reid (D-Nev.) recounted how Biden’s Washington life began after his first wife, Neilia, and daughter were killed in a car crash just before Christmas 1972, weeks before he was to be sworn into the Senate. “Joe Biden’s life is the stuff of which movies are made,” he said.

Reid wiped tears from his eyes as McConnell quoted a favorite Biden line regularly attributed to his father: “Champ, the measure of a man is not how often he is knocked down, but how quickly he gets up.”

Sen. John McCain (R-Ariz.), with whom Biden has engaged in furious battles over foreign policy over the past 30 years, told the story of being a Navy officer helping lead a congressional delegation overseas that included a night in which McCain drank too much and ended up dancing on a table — with Jill Biden, the vice president’s wife.

In an August interview, Biden told The Post that he did not plan to campaign in Arizona against McCain, but if his race got close and Biden had to go, he would not say a bad word about McCain. The 80-year-old incumbent won easily, and Biden never stumped against his friend.

“We’ve both been privileged to know members of this body who were legends in their own time, and are remembered as important historical figures. But I haven’t known one who was a better man than you,” McCain said Wednesday.

Leaving the tribute, Biden beamed with pride. “This is the Senate that I know and I love. The generous remarks were not deserved but were well appreciated,” he said.