“They should aggressively pursue him,” Lott told The Hill, offering advice to his former colleagues in leadership and those close to the former Democrat-turned-Independent.

With Election Day around the corner, speculation has intensified about whether Lieberman will cut his last ties to Democrats and either join the Republican Party or caucus with the Senate GOP, thus narrowing the Democratic majority in the upper chamber and possibly denying Democrats the 60 votes they need for a filibuster-proof majority.

“If the Democrats take away his credentials or they take away his committee, why would he want to make them a majority?” Lott asked.

Lott, who participated in successful efforts to convince lawmakers such as Sen. Richard Shelby (Ala.) and then-Sen. Ben Nighthorse Campbell (Colo.) to switch from Democrat to Republican, said Lieberman would be a boon to the Senate GOP.

“We need different points of view and Joe would bring that,” said Lott, now a lobbyist at the Breaux-Lott Leadership Group, a firm he founded with former Sen. John Breaux (D-La.).

Lieberman bolted from the Democratic Party in 2006 after being bested by Ned Lamont in a close primary election that centered on the Iraq war, which Lieberman supports. After the primary, Lamont secured the endorsements of Senate Democratic leaders but Lieberman won a rematch in the general election running as an Independent.

Lieberman has caucused with Democrats since his reelection but has endorsed and campaigned for McCain, criticized Democratic presidential nominee Barack Obama and been a staunch ally of the GOP on the war in Iraq and U.S. foreign policy.

Lieberman’s actions on McCain’s behalf, and his attacks on Obama, have generated anger among Senate Democrats and demands that he be punished.

If McCain wins the presidency, Lieberman is seen as a candidate for a cabinet position, such as secretary of defense, which would end his Senate career. If Obama wins, Senate Democrats – and Lieberman – face difficult decisions.

Lieberman has remained a reliable Democratic vote on domestic matters, however, and holds views on issues such as abortion and organized labor that are anathema to most Republicans.

“Clearly,” Lott said, Lieberman’s positions on many issues are “more liberal than most Republicans'.”

Lott pointed to the presence of three centrist Republicans in the Senate as evidence of the party’s diversity.

“The Republican Party is not a totally homogenous organization,” Lott added. “You can ask the two ladies from Maine, Olympia [Snowe] and Susan [Collins], or you can ask Arlen Specter” of Pennsylvania, he said.

Conservative activists and commentators have denounced centrist GOP lawmakers such as these as “Republicans in Name Only,” or RINOs, and are likely to react similarly to Lieberman.

Lott rejected that attitude. “I don’t agree with those who say you’ve got to be a total, pure Republican on every issue,” he said.