President Barack Obama has been campaigning in Massachusetts before a special election to fill the Senate seat previously held by the late Senator Ted Kennedy.
Democratic Party candidate Martha Coakley and Republican Scott Brown are reportedly neck and neck in opinion polls.
The BBC reports defeat for the Democrats on Tuesday could block the Obama healthcare bill.
Mr Brown has promised to vote against it and his victory could deprive the Democrats of the 60-vote majority they need to pass that and other legislation.
The Obama administration has made healthcare reform its top domestic priority.
The special election will be held a day before the first anniversary of Mr Obama's inauguration.
The BBC reports Mr Brown has been able to tap into voter anger and anxiety over federal spending, expanded government and high unemployment, as well as healthcare reform.
Since Kennedy's death last August, the seat has been held by an interim appointee, Senator Paul G Kirk Jr.