The Bloomberg group includes several top-level operatives who played key roles in the mayor’s decisive re-election last year or who are in the administration, and have taken leaves from their jobs to work on Mr. Lieberman’s campaign....

Since Mr. Lieberman lost the Democratic primary in Connecticut to Ned Lamont, they have helped open campaign offices, devised a strategy to reach voters and are corralling enough volunteers to cover 2,800 shifts at more than 700 polling sites on Election Day, Nov. 7.

Tammy Sun, a spokeswoman for Lieberman, said Friday that they would not participate in the debate.

"All three candidates agreed to three debates, and we will be sticking to that agreement even if others choose to break it," Sun said. At Monday's debate Lamont and Schlesinger urged further debates while Lieberman sat quietly. Schlesinger asked him directly if he would participate and Lieberman appeared to nod affirmatively.

However, when asked the next day by reporters if a fourth debate was in the making, Lieberman said it wasn't likely.

Schlesinger said Thursday he is spending $50,000 per week for the new ads and insisted he believes they will make a major impact, though Democrat Ned Lamont and incumbent Sen. Joseph I. Lieberman each have been spending 10 times that amount on TV for weeks.