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Mr. Lieberman has a mixed record on supporting the Democratic majority on cloture votes in the current Congress. He voted to support a Republican-led filibuster blocking votes to end the war in Iraq and to censure former Attorney General Alberto R. Gonzales, but voted to end a filibuster on a major overhaul of immigration laws.

But Mr. Dautrich said Mr. Lieberman could have real leverage in a potential Obama administration on high-profile votes such as health care reform or Supreme Court nominees, where the filibuster threat gives the minority party real bargaining power.

Nevada Sen. John Ensign, head of the National Republican Senatorial Committee, said in an interview on MSNBC Monday the Republican Party would welcome Mr. Lieberman “with open arms” if the Democrats spurn him.

Mr. Ensign conceded there was a “fair possibility” the Democrats will get or come close to the magic 60-vote total.

“Joe is certainly going to be a wild card in there,” he said.