Each candidate was scheduled to hold seven campaign events Tuesday, mostly in North Jersey.
"We're paying special attention to voters who are likely to vote for Mayor Booker but who may need a little extra encouragement to get to the polls," said Booker spokesman Kevin Griffis.
The campaign is also e-mailing voters a video released Monday in which Obama urges people to vote for Booker.
Lonegan spokesman Will Gattenby said the campaign is focused on "turning out the vote from a grassroots level."
"When Mayor Booker was taking the people of his state and his city for granted, Mayor Lonegan was on the streets of every county in New Jersey meeting the voters, recruiting volunteers, and building an unbeatable coalition of supporters," he said in an e-mail.
Many polls show a tighter-than-expected race for Booker, a rising star in the Democratic Party whom political observers expected to win by roughly 20 points. New Jersey voters have not elected a Republican to the Senate since 1972.
A Quinnipiac University poll released Tuesday gave Booker a 14 percentage point lead among likely voters. "It's a New Jersey habit, electing Democrats to the Senate," said Maurice Carroll, director of the Quinnipiac University Polling Institute.
Two polls released a day earlier showed Booker leading by 10 points and 22 points, underscoring the difficulty of making predictions.
"New Jersey has no precedent for modeling a likely electorate in a special statewide election," Patrick Murray, director of the Monmouth University Polling Institute, wrote in a blog post Tuesday. "Especially one that occurs just three weeks before the regular general election. And doubly so for one that occurs on a Wednesday rather than a Tuesday."
Murray said Monmouth's likely voter model indicated turnout would be from 35 percent to 40 percent of registered voters. About 215,000 people voted for Booker in the Aug. 13 Democratic primary, exceeding analysts' expectations. Fewer than half that number turned out for Lonegan in the GOP primary.
According to Murray, just under 50 percent of New Jerseyans have voted in recent years in elections in which the ballot is headed by a Senate or gubernatorial race.
Two recent special elections in Massachusetts also may offer clues to what to expect Wednesday.
In January 2010, Massachusetts held a special Senate election for the seat of the late Democrat Edward M. Kennedy, seen in part "as a referendum on Obama - an issue the Lonegan camp hopes will factor into the New Jersey election," Murray said. Republican Scott Brown won with a 54 percent turnout.
In another Massachusetts special Senate election in June, to replace Democrat John Kerry, who became secretary of state, only half as many voters turned out, according to Murray. Longtime Democratic Rep. Edward Markey won the contest.
The Booker campaign expects a largely Democratic turnout with fewer independents heading to the polls than in presidential years, noting that Democrats far outnumbered Republicans and unaffiliated voters in 2011, 2010, and 2009.
Polls are open from 6 a.m. to 8 p.m.