Scott Brown eyes second Senate upset, this time in New Hampshire
Republican candidate for the United States Senate Scott Brown (L) is joined by U.S. Senator John McCain (R-AZ) at a campaign stop at the American Legion Post #3 in Nashua, New Hampshire October 27, 2014. REUTERS/Brian Snyder

Scott Brown, a Republican who stunned Massachusetts Democrats in 2010 when he won the U.S. Senate seat that Edward Kennedy had held for half a century, could notch another upset on Tuesday as he takes on Senator Jeanne Shaheen of New Hampshire.

Polls show a dead heat between Shaheen, a first-term senator and former governor, and Brown, who had been a little-known state legislator before his surprise 2010 victory.

Turnout was unusually high for a midterm election, officials said, with Secretary of State Bill Gardner estimating it could top 50 percent, which would be a record for a non-presidential year.

Brown lost his first re-election bid to Elizabeth Warren in 2012 and moved to New Hampshire early this year. He has sought to tie Shaheen closely to President Barack Obama, who is unpopular in this state, while Shaheen has depicted her rival as out of touch on women's issues.

Polls have shown Brown, 55, closing in on Shaheen, 67, since he disclosed in March he was considering a run.

A WMUR/University of New Hampshire poll released on Sunday showed the two in a statistical tie, with 49 percent of 757 likely voters saying they planned to vote for Shaheen and 48 percent for Brown. When asked who they thought would win the race, 55 percent bet on Shaheen, with just 30 percent predicting a Brown victory.

"We don't know what will happen to him in the election, but I think that either way he is an up-and-comer in the national Republican Party," said Neil Levesque, executive director at the New Hampshire Institute of Politics. "He's done better than most people thought he would."

Both Brown and Shaheen staged a campaign blitz over the past few days, with former Secretary of State Hillary Clinton stumping for Shaheen over the weekend.

"Either we're all in this together, or we're all in this on our own," Clinton, who is considering a 2016 presidential bid, told Shaheen supporters.

Both parties see the seat as critical to taking a majority in the Senate, which Democrats now control. But the big names in both parties have an extra incentive to travel to the state, which holds the first presidential nominating primary.

Potential Republican White House hopefuls, including New Jersey Governor Chris Christie and U.S. Senator Rand Paul of Kentucky, visited to endorse Brown.

Brown had a moderate record in Massachusetts and has made some headway with Democratic voters in New Hampshire, polls show.

Voters largely echoed their candidates' pitches in explaining their picks.

After casting his vote at a Nashua school, 82-year-old Roger Theriault said he regarded Shaheen as following in lockstep with Obama.

"She's too close to him," Theriault said.

Jerri Dalessio, 68, said she was skeptical of Brown's ties to the state where he grew up but only returned to this year.

"I just think Shaheen supports New Hampshire," Dalessio said.

(Reporting by Ted Siefer; Writing by Scott Malone; Editing by Jill Serjeant and Doina Chiacu)