Voters thronged to the polls in Massachusetts Tuesday in a special election Republicans hope will be a national game-changer, slowing down President Barack Obama's agenda and loosening the Democratic grip on the U.S. Senate.

As dawn broke in the frosty Northeast, the GOP publicly relished the possibility that a previously obscure state senator, Scott Brown, could wrest the election from Democrat Martha Coakley, considered the overwhelming favorite until just a few days ago.

In contrast to the light turnout for the party primaries last month, both candidates expected a heavy turnout following the national attention thrust upon their race. There was a clear sign at one polling place: A line of cars stretched for nearly a half-mile from the gymnasium at North Andover High School, the polling place for a community of about 30,000 about a half-hour north of Boston. Some drivers turned around in exasperation.

Speaking to reporters after she voted early Tuesday at an elementary school near her home, Coakley voiced confidence that she would win, saying "we've been working every day."

She said "we're paying attention to the ground game. ... Every game has its own dynamics. ... We'll know tonight what the results are." The polls close at 8 p.m. EST.

Brown, driving his pickup truck to a polling place to vote, played down the import of becoming the 41st Republican vote to uphold a filibuster, telling reporters, "It would make everybody the 41st senator, and it would bring fairness and discussion back to the equation."

He also said that should he win, he hoped Democrats controlling the state's election apparatus "would do the right thing and certify me as quickly as possible."

While there were signs of a heavy turnout, including 500 ballots through the machine that counted Brown's about 9:45 a.m., he dismissed polls showing a swell of support for him.

"I've never been a big poll person," he said. "I'm up in some, I'm down in some. And we'll see what happens, 8:01 (p.m.)."

Voters faced backups at some polling stations. And election officials in Boston said the turnout was more than twice the voters recorded in December's party primaries. Secretary of State William Galvin says he expected from 1.6 million to 2.2 million people to vote - a spread of between 40 percent and 55 percent of registered voters.

A light snow started falling steadily shortly after the polls opened north of Boston, covering roads and sidewalks with a slippery coating. Some voters in Haverhill, about 35 miles north of Boston, grumbled as they navigated snow banks and thick slush to get to the polls. National Weather Service meteorologist Charlie Foley called it "kind of an annoyance."

In Washington, senior White House adviser David Axelrod said the White House expects Coakley to win. Axelrod said Obama, who campaigned with Coakley Sunday in Boston and cut a last-minute ad, did everything he could to help.

"I think the White House did everything we were asked to do," Axelrod told reporters. "Had we been asked earlier, we would have responded earlier. But we responded in a timely fashion when we were asked."

In the race to fill the late Sen. Edward M. Kennedy's Senate seat, Republicans want Brown to become their 41st vote in the 100-member Senate. That would give them enough votes to successfully filibuster Democratic initiatives, including the massive health care bill that majority Democrats are rushing to finish.

"I think it's been a fascinating process to watch unfold," said Republican Party Chairman Michael Steele. "A year ago, the landscape was very different."

Former Democratic chairman Terry McAuliffe said his party must have a strong turnout, acknowledging "an anti-incumbency mood out there."

The swift rise of Brown has spooked Democrats who had considered the seat one of their most reliable. Kennedy, who died in August, held the post for 47 years. The last time Massachusetts elected a Republican to the U.S. Senate was 1972.

Brown has tried to turn Democrats' expectation of an easy win to his advantage, proclaiming, "It's not the Kennedy seat, it's the people's seat."

It's unclear whether a full-court press by unnerved Democrats was enough to blunt the surging Brown.

A Suffolk University survey taken Saturday and Sunday showed Brown with double-digit leads in three communities the poll identified as bellwethers: Gardner, Fitchburg and Peabody. But internal statewide polls for both sides showed a dead heat.

For Brown's staunchest supporters, such as Glen Stump, 47, a software engineer from Andover, Democrats' appeals fell on deaf ears.

"I hope he can stop this Obamacare legislation," Stump said, using critics' nickname for the health care overhaul bill. "I think it's being run in a completely partisan manner."

A third candidate, Joseph L. Kennedy, a Libertarian running as an independent, said he's been bombarded with e-mails from Brown supporters urging him to drop out and endorse the Republican. Kennedy, who was polling in the single digits and is no relation to the late senator, said he's staying in.