Lamont and Republican Alan Schlesinger, meanwhile, have accepted an invitation to a fourth debate Thursday, but Lieberman declined. His press secretary, Tammy Sun, said the campaign was sticking to the agreement to hold three debates.

Lamont campaigned Thursday at the port of New Haven with DeStefano, the city's mayor and the Democratic gubernatorial nominee. They talked about dwindling federal homeland security money.

They criticized Lieberman and Rell for a 60-percent reduction in Connecticut's homeland security funding.

New Haven harbor is the busiest port in all of New England, said DeStefano, and the second largest storage place for the Northeast petroleum reserve.

"We have tried to get this right since 2001, and since 2001, frankly, the intent and the ability to secure our infrastructure has degraded," DeStefano said.

Her visit came a day after U.S. Sen. John F. Kerry, D-Mass., campaigned with Lamont. Sen. Barack Obama, D-Ill., who urged support of Lieberman before the primary, sent an e-mail appeal on Lamont's behalf.

"I would say most of my Senate Democratic colleagues have stayed out of this race, and that, too, means something to me," Lieberman said. "But I have a special place in my heart for Mary and the other four who stuck with me in the general election."

Lamont aides said they welcomed the support of Obama, who has enjoyed a surge in popularity in recent weeks as speculation about his national ambitions mounts.

"He's a very credible, charismatic and inspiring politician," said senior Lamont adviser Tom D'Amore. "We're thrilled to have his support.

Obama has also given $5,000 to Lamont's campaign through a political committee.

"If he's elected it will be with Republican money," Lamont said. "I don't know where he'd be on the issues. When the next Supreme Court nomination comes, where will the senator be? I don't know. When it's time to redeploy troops, where will the senator be? I don't know. When it comes to constitutional rights, detainee treatment, he's been on the wrong side of history."

Lamont later added, "Dick Cheney has campaigned around the country talking about Joe Lieberman. He knows something."

“Joe Lieberman is masquerading as a Republican,” he said.

The senator rarely mentions Mr. Schlesinger on the stump, and the Lieberman campaign has largely ignored his entrance into the race, except to assert that the Republican has become something of a folk hero among some Lamont supporters.

But in a nod to the closeness of the Senate race, and the potential for even a small uptick in Mr. Schlesinger’s fortunes to alter his own, Mr. Lieberman has recently argued that a vote for the Republican would help only Mr. Lamont.

“With all respect to Alan Schlesinger,” Mr. Lieberman said last week, “this race is effectively a race between Ned Lamont and me, so a vote for Alan Schlesinger helps Ned Lamont.”