MINNEAPOLIS — The only trace of the vice president came on a candy wrapper.

Joe Biden may be considering whether to enter the race for president, but he sat out last week’s meeting of the Democratic National Committee. In his place, backers greeted a curious few in a hotel suite 20 floors above the official gathering, handing out chocolate bars wrapped with a stylized photo of Biden behind the wheel of a convertible and an “I’m Ridin’ with Biden” label.

In any other year, a sitting vice president would have headlined such a meeting as the heavy favorite for the party’s nomination. Instead, the gathering served as proof that if Biden choses to run, he’ll do so as an underdog to Hillary Rodham Clinton.

Clinton’s years-long flirtation with a second White House campaign — time her allies used to lock up support of much of the Democratic Party’s leadership — and her undeniable political celebrity have upended the traditional script. Rather than inheriting his party’s machine, a Biden campaign would have to find a way to take it back.

“Secretary Clinton’s folks have been talking to these people for a very, very long time,” said Vermont Sen. Bernie Sanders, whose vibrant crowds and steady poll numbers make him Clinton’s strongest current challenger. “So she has a huge advantage.”

Yet Biden’s supporters see an opening, due in no small part to Clinton’s inability to shake questions about her use of a personal email server while serving as secretary of state. His candor, long history of fighting for Democratic causes and personal struggles — a widower at a young age now grieving over the recent death of his son Beau — make him an admired figure in the party.

“He’s one of us. He gets it,” said Jon Cooper, a supporter who this summer began working with a group encouraging Biden to enter the race. “Everybody likes Joe Biden.”