The Delaware senator noted that Democrats Al Gore and John Kerry were also well ahead in polls just weeks before Election Day in 2000 and 2004, but both lost their presidential contests to President Bush.
"We've been here before. We've been poised to win the presidential election," Biden said. "The last two times we underestimated how successful virulent attacks are."
Biden spoke to about 150 Democratic donors at a luncheon fundraiser at the home of former state controller and gubernatorial candidate Steve Westly in Atherton, a wealthy Silicon Valley suburb.
The vice presidential candidate warned supporters that the campaign will get "ugly" over the next 17 days, noting that Republican John McCain's campaign has started making automated telephone calls "sending in the most scurrilous stuff you've heard."
In recent days, senators from both parties have asked the Arizona senator to stop using "robo-calls" that link Obama to former 1960s radical William Ayers.
Biden told supporters Saturday he believes he and Obama will ultimately prevail, but the new administration will be "left with the greatest amount of challenge that any president has had since Franklin Roosevelt was elected president."
"Anybody who thinks we're going to be elected and all of a sudden the birds are going to start chirping ... is wrong," he said.
Biden said if they're elected, he and Obama would assemble "one of the finest economic teams in the history of this country" to ensure that the United States remains a leader in the 21st century. He said "the underlying elements of this economy are in real trouble."