New York City voters will elect a new mayor for the first time since 2001 and are likely to elect the first Democrat for that spot since 1989.
This off-year election, which is expected to draw a low turnout, also features mayoral races in Detroit and elsewhere, special congressional elections in Alabama and five other states, state legislative votes, citizen initiatives and a variety of state and local referendums.
In Virginia, former Democratic National Committee Chairman Terry McAuliffe is favored to defeat conservative Republican state Attorney General Ken Cuccinelli in replacing Republican Gov. Bob McDonnell.
"If mainstream Virginians from both parties don't turn out to vote, you're letting the Tea Party decide Virginia's future," McAuliffe said at a rally with Biden in Annandale, near Washington.
"That's why I need your help more than ever," he said. "Get! Out! The votes!"
A Quinnipiac University poll released Monday showed McAuliffe at 46 percent, Cuccinelli at 40 percent and Libertarian Robert Sarvis with 8 percent among likely voters. The poll had a 2.5 percentage point margin of error.
But Biden warned Democrats not to get comfortable with a 6-point lead.
"Don't take this for granted," Biden said.
"There's only one place the Tea Party can compete with us -- and that is, they do turn out their base," he said.
Cuccinelli, who trailed McAuliffe by 4 points in a Quinnipiac survey last week, said the election is a referendum on the troubled U.S. healthcare overhaul.
"Virginia is the next battleground in America on 'Obamacare,'" he said at a Warrenton rally. "So ... let's send them a message loud and clear: Virginia says no to Obamacare. And Virginia says no to expanding Obamacare."
Sen. Marco Rubio, R-Fla., campaigning with Cuccinelli, told Latinos in Spanish: "We don't want Obamacare [and] we don't want more big government. We want more leaders like your next governor, Ken Cuccinelli."
Farther north, Republican incumbent New Jersey Gov. Chris Christie maintained a nearly 2-to-1 lead, or 61 percent to 33 percent, over little-known Democratic challenger state Sen. Barbara Buono among likely voters, a separate Quinnipiac poll released Monday indicated.
That poll had a 2.6 percentage point margin of error.
"We can't take anything for granted," Christie said at a campaign stop. "We are Republicans in New Jersey," a state that traditionally votes Democratic.
Buono, at her final stop Monday, said a new book about Republican Mitt Romney's failed presidential bid said the former Massachusetts governor didn't pick Christie as his running mate in part because his background was "littered with potential land mines."
"They vetted him for vice president and they went through it very, very carefully. They asked him a lot of questions, they didn't like all the answers they were getting," she said in remarks quoted by The (Newark) Star-Ledger.
"And they disqualified him to run for higher office," Buono told supporters. "So, if he's not good enough for Romney, he's sure as hell not good enough for New Jersey."
New York City appears poised to elect Democratic city Public Advocate Bill de Blasio by a sweeping margin over GOP contender Joe Lhota, former head of the state Metropolitan Transportation Authority.
A Monday Quinnipiac poll showed de Blasio ahead of Lhota 65 percent to 26 percent, with Independence Party candidate Adolfo Carrion at 3 percent. The poll had a 3.6 percentage point margin of error.
A de Blasio win would give New York City its first elected Democratic mayor since David Dinkins was elected in 1989.
Republican Rudolph Giuliani was elected in 1993 and re-elected in 1997. Republican Michael Bloomberg was elected in 2001 and re-elected in 2005. He left the Republican Party in 2001 and successfully persuaded the City Council to extend the city's term limits law so he could run for a third term.
He was re-elected as an independent on the GOP and Independence and Jobs & Education ballot lines in 2009.
The term-limits law was changed back to two terms in 2010.
Detroit's mayoral race is non-partisan, with candidates not listed by political party. The key campaign issue is the city's bankruptcy.
Businessman Mike Duggan, who ran a write-in primary campaign and received 46 percent of the vote in an Aug. 6 primary, and Wayne County Sheriff Benny Napoleon, who won 30 percent of the primary vote, are battling to replace Mayor Dave Bing, who is retiring.
Duggan and Napoleon spent the final hours of their campaign Monday pressing the flesh and pressing their message that they were best qualified to lead the city during its bankruptcy, while state-appointed Emergency Manager Kevyn Orr manages the city's financial operations through at least September 2014.
Detroit in July became the largest U.S. city to file for bankruptcy.
Polls showed Duggan with a nearly 2-1 lead over Napoleon, but Napoleon told the Detroit Free Press he was confident the race would be much closer than that.
Other big cities having mayoral races include Atlanta, Boston, Cleveland, Houston, Los Angeles, Miami, Minneapolis and Seattle.
Alabama will hold one of the nation's six special congressional elections Tuesday. It will be a Republican primary pitting establishment GOP candidate Bradley Byrne against Christian conservative Tea Party hopeful Dean Young to fill the seat vacated by Republican Rep. Jo Bonner, who resigned Aug. 2 to become University of Alabama vice chancellor.
Bonner backs Byrne, calling him a candidate "in the mold" of all the district's previous representatives.
Polls indicate the special election -- a runoff from a Sept. 24 primary -- could go either way. The winner in the strongly Republican 1st Congressional District is widely expected to win the general election Dec. 17.
A Byrne victory could lend momentum to a GOP establishment effort to regain control of the party from the Tea Party faction, The Washington Post said.
Other special congressional elections are being held in Illinois, Massachusetts, Missouri, Louisiana and South Carolina.
Eligible Connecticut voters will be able to register Tuesday and then vote immediately, as the state becomes the 11th in the country to enact Election Day registration.
Democratic Gov. Dannel Malloy said, "Same-day voting helps to ensure that all citizens have a voice in their government."
Elsewhere, Colorado voters will decide Tuesday whether to place a 25 percent tax on recreational marijuana.
Proposition AA would impose a 15 percent excise tax on wholesale purchases and another 10 percent state sales tax for retail purchases.
The excise-tax money would go toward school construction, as part of the 2012 constitutional amendment that legalized recreational pot sales, The Denver Post said.
At the same time, 11 counties in northern and eastern Colorado are to hold non-binding votes on seceding from the state and creating a 51st state called North Colorado.
The initiative stems from a philosophical divide between Colorado's rural population and the state Legislature over issues such as gun control and renewable energy, the Post said.
The secession move would need the OK from the Legislature and governor, as well as the U.S. Congress.
Critics say congressional lawmakers would never allow the creation of a 51st state, if the idea even reaches them, the Post said.