BOSTON -- In what could potentially be a history-making race, millions of Massachusetts voters were braving snow and slush to get to their polling places Tuesday as the state chooses a replacement for longtime Sen. Ted Kennedy, possibly casting ballots that could send a Republican to Washington from one of the bluest states in the union.

Kennedy died last August after a long battle with brain cancer after representing the Bay State for 47 years.

Democratic Attorney General Martha Coakley, who had the backing of President Barack Obama and the Kennedy family, was thought to be his shoo-in successor until only a week ago when little-known GOP state Sen. Scott Brown began surging in the polls.

In a tight race, there were some reports of discrepancies at polling places, with Secretary of State William Galvin investigating reports that two ballots had been pre-marked for Brown, one in Cambridge and one in Boston's Brighton neighborhood. He said the ballots had been located and voided.

Galvin called voter turnout "brisk," despite the snowy weather. Some suburban towns estimated voter turnout as high as 70 to 75 percent.

"We're seeing a very good turnout considering the weather circumstances we're working under. There's a high level of interest. We're particularly seeing a high level of interest in some of the suburban communities. Traditionally, cities tend to vote somewhat later, but we have seen a number of communities, lines and people standing in lines, very patiently in the snow," Galvin said.

In Boston, Galvin said, officials were seeing more than double the turnout they saw during the senate primary in December. Boston Mayor Tom Menino said that as of 6 p.m., about 33 percent of register voters cast ballots.

In Dover, a community southwest of Boston, officials said they were seeing almost 75 percent turnout.

Coakley, along with her husband, cast her ballot early near her Medford home, while Scott Brown drove his green pickup truck to his polling place in Wrentham, accompanied by his daughters.

After voting, Coakley campaigned at Boston's busy North Station MBTA stop to try to energize her base. She shook hands and greeted commuters, some of whom said they remained undecided.

"I wish her all the best and she has my vote," one voter said.

"We're feeling great," Coakley said, downplaying reaction in Washington to her slide in the polls and fears for Obama's healthcare agenda should she lose.

"They're going to pay attention to what they need to do and I've been paying attention to what I need to do to get our vote out today and we're going to win today," Coakley said.

Brown appeared relaxed as he cast his ballot, despite a crush of reporters and supporters at his Wrentham precinct.

"I just went to the gym, I had a nice workout. I'm very excited to be here and vote as I have done for every election since I was 18," he said.

He said the truck that brought him there had become a "symbol of a regular guy from Wrentham making an effort and trying to bring some balance back to Washington."

Brown, who would become the GOP's 41st senator in Congress if he were to win the race, loosening the Democratic hold on Capitol Hill, said he did not see the election as a referendum on Obama's health care initiative.

"I would be the 41st senator, but it would make everybody the 41st senator, and it would bring fairness and discussion back to the equation, and that's good for America. That's just good for democracy, to have good government, to have people talking. Instead of back room deals, we're talking about transparency and doing it the right way," Brown said.

The last time Massachusetts elected a Republican to the senate was in 1972.

A third candidate is running in the race, Joseph L. Kennedy, who is no relation to Ted Kennedy. The independent said he has been bombarded with e-mails asking him to drop out but has declined to do so.