Polls show that Lieberman, who was Al Gore's vice presidential running mate in the 2000 presidential race against Bush, trails challenger Ned Lamont by double digits in the Democratic primary, with polls open Tuesday.
The outcome of the primary election was expected within a few hours of the polls closing late Tuesday.
Lieberman, a relative hardliner among Democrats on defence and foreign policy, backed Bush's decision to invade Iraq in March 2003. During his summer election campaign, Lieberman cited his record of criticizing the Bush administration for mistakes in Iraq while defending his vote for the war and continued support for staying in Iraq.
Lieberman also argued that he has opposed Bush domestically on social and economic policies.
If he loses the nomination, Lieberman has indicated that he will run as an independent in the November general election - a move that makes Democratic party strategists uneasy because it could split the Democratic vote in favour of the centre-right Republican Party's candidate.
However, recent polls have suggested that Lieberman could be a favourite to win the general election as an independent in Connecticut, a small, socially liberal state east of New York City.
Republicans hold majorities in both houses of Congress, but Democrats are hoping that increasing public criticism of the war in Iraq, as well as dissatisfaction with ethics scandals and other image problems for Republican legislators, will give them a chance to reclaim both the Senate and the House of Representatives.
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