What looked likely to be a Democratic shoo-in to replace late party icon Edward Kennedy has instead turned into a too-close-to-call race with a last-minute rally by a Republican, State Senator Scott Brown, a relative unknown just weeks ago.

Latest polls suggest he could defeat state Attorney General Martha Coakley, which would be a huge upset in this traditionally liberal New England state, take away the Democrats' supermajority in congress and thereby reshape President Barack Obama's agenda after just one year in office.

Kennedy, who held the seat for almost 47 years, died in August of brain cancer. Massachusetts last elected a Republican to the Senate in 1972, but the weak economy and doubts about the healthcare overhaul have moved voters to reconsider political loyalties passed down through generations.

Their possible change of heart could not have come at a more crucial juncture for Obama.

Democrats now control 60 votes in the Senate to 40 for the Republicans. The loss of one seat could hamper the Democrats' ability to cut off debate and proceed to a vote on the biggest healthcare reform in the United States in more than four decades.

More broadly, an upset in Massachusetts, or even a narrow win for Coakley, would raise the spectre of large Democrat losses in mid-term congressional elections in November.

Voter turnout is frequently low in off-season elections, and can be even lower due to bad weather. A messy snowstorm hampered travel on Monday and snow showers might fall on Tuesday.

Polls will be open from 7 a.m. until 8 p.m. ET (12:00 a.m. to 1:00 a.m. British time on Wednesday). Given the likely closeness of voting, it could take officials a few hours to declare the winner.

'ANGER AND FRUSTRATION'

The Republican has attracted strong support from independent voters, including many who backed Obama in 2008.

"There's an anger, a frustration that's being felt in Massachusetts," said James Gomes, director of the Mosakowski Institute for Public Enterprise at Clark University in Massachusetts.

Millions of dollars have flooded into the state of 6.5 million people to buy all day television advertising for both sides, transforming a relatively sleepy contest into a bitter brawl.

Coakley has been criticized for a lacklustre campaign. She took almost a week off from the campaign trail around Christmas, at a time when Brown's appeal was on the rise.

Democrats in Massachusetts have a large advantage in registered voters and a more tested get-out-the-vote apparatus that can be swung into action on Tuesday.

But Republicans appear to be motivated in the final stretch.

"I would expect that the Democrats would have an advantage in terms of the shoe leather on the pavement. But it sure looks like the intensity is on the Republican side right now," Gomes said.