Barack Obama, the US president, has championed healthcare reform and different versions of a healthcare bill have passed initial votes in the House of Representatives and Senate.
The reforms are backed by Democrats but opposed by Republicans and a defeat in Massachusetts would cost the Democrats their 60-vote Senate majority, which prevents Republican use of a filibuster, a procedure used to stall and defeat legislation.
Brown has said that he will oppose the healthcare bill - reviewed versions of which need to be passed once more in both houses of congress before being signed off by Obama.
More broadly, an upset in Massachusetts - or even just a narrow win for Coakley - would raise the possibility of large Democrat losses in mid-term congressional elections in November.
Pre-poll estimates last week showed gains for Brown, including taking 20 per cent of Obama's presidential poll supporters, compared to Coakley having four per cent of John McCain's, the Republican presidential nominee's.
If the Democrats lose their Senate super-majority they would have to gain support from a moderate Republican or pass the version of the bill already approved by the Senate.
This version is viewed to have made greater concessions to skeptics than the bill passed by the House of Representatives. The upcoming votes in congress aim to reconcile the two versions.
Obama steps in
In a mark of the importance of the vote, Obama joined Coakley to campaign in Boston on Sunday, despite foreign policy concerns with the recent Haiti earthquake and other pressing issues.
Massachusetts, which has not had a Republican senator for 38 years, has three registered Democrats for every Republican, however, there are a greater number of independents.
Joseph Kennedy an independent, Libertarian candidate who is no relation to Edward Kennedy, is also running and rejected appeals by Republican supporters to drop out of the race and back their party.
Massachusetts senator Edward Kennedy, who had campaigned for decades for greater access to public healthcare, died in August after nearly 47 years in office.
Polls are to close at 8pm (01:00GMT on Wednesday) with a winner to emerge a few hours later.