With promises of money and personal campaign appearances, Democratic leaders rallied today behind the campaign of Ned Lamont, the anti-Iraq war challenger who defeated Senator Joseph I. Lieberman in the Connecticut primary, leaving Mr. Lieberman increasingly isolated as he pledged to forge ahead as an independent candidate.

At the same time, Republicans began a concerted effort to use Mr. Lieberman’s defeat to portray Democrats as weak on national defense, reprising a theme that they made central to the last two national campaigns. The attacks often came in searing remarks from, among others, Ken Mehlman, the chairman of the Republican National Committee, and Vice President Dick Cheney, who went so far as to suggest that the ouster of Mr. Lieberman might embolden Al Qaeda terrorists.

“It’s an unfortunate development, I think, from the standpoint of the Democratic Party, to see a man like Lieberman pushed aside because of his willingness to support an aggressive posture in terms of our national security strategy,’’ Mr. Cheney said in a telephone interview with news agency reporters.

Howard Dean, the Democratic national chairman, called on Mr. Lieberman to quit the race, and in an interview said he would be disappointed in any Democratic Party leader who continued to support Mr. Lieberman, declaring they “have an obligation” to support their nominee.

But most Democrats were united in saying they would not pressure Mr. Lieberman to step aside for now, saying he was too angered by his loss to accept such counseling and noting Republicans as of now do not have a strong candidate who could take advantage of a fractured Democratic field.

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Mr. Lieberman has said he will vote with the Democratic caucus if he is elected as an independent, a consoling thought for Democrats contemplating a Lieberman victory in November.

“If he wants to talk to me about it, fine,” said Senator Christopher Dodd, the Connecticut Democrat who was one of Mr. Lieberman’s close advisers and friends, and who endorsed Mr. Lamont today. “It’s not up to me to call. I regret he made that decision but it’s pretty firm: I don’t think there’s any way to talk him out of it.”

With the Iraq war now dominating the international stage, and Republicans again trying to turn it to their advantage by casting it as central to protect American from terrorism, Mr. Dean and other Democrats pushed back, declaring that voters would not buy the Republican argument in yet another national election.

The attacks came as Republicans have been openly alarmed that their party is heading for big losses this November. Republican polling has also said that national security was the most effective issue Republicans have to motivate their base voters.

“It’s right-wing propaganda,” Mr. Dean said. “They are beginning to look ridiculous: A majority of Americans now believe that going to Iraq was the wrong thing to do. I think this shows how far out of touch the Republicans are: What you are seeing is the beginning of the end of the Republicans because a lot of this was a referendum on George Bush’s policies. George Bush is going to take a big hit and a lot of people are going down with him, including Ken Mehlman.”

Mr. Lieberman dismissed the significance of the kind words from the White House, as well as its criticism of his party based on his loss. “That’s not my fault,” he said. “They are not criticizing me for running an independent campaign, they are criticizing Democratic voters for the way they voted.”

There was little question that Democrats were united in their decision to back Mr. Lamont, no matter their apprehensions about his skills as a campaigner, his credentials or some of his ideological positions.

Senator Hillary Rodham Clinton of New York, who had backed Mr. Lieberman in the primary, said she had donated $5,000 to Mr. Lamont’s campaign and suggested she was prepared to campaign with him. Former President Bill Clinton, whose campaign appearance with Mr. Lieberman was described by the senator as an emotional turning-point his campaign, issued his statement affirming his support for the Democratic nominee.

Harry Reid of Nevada, the Senate Democratic leader, and Senator Charles E. Schumer of New York, the head of the Democratic committee for Senate candidates, described Mr. Lieberman’s loss as encouraging news for Democrats going into the fall elections.

“The perception was that he was too close to George Bush, and this election was, in many respects, a referendum on the president more than anything else,” Mr. Schumer and Mr. Reid said in a joint statement. “The results bode well for Democratic victories in November.”

Mr. Dean, whose brother James was a prominent supporter of Mr. Lamont, said Mr. Lieberman was being “disrespectful of Democrats and disrespectful of the Democratic Party” by saying he would stay in the race as an independent.

“It was decided in Joe’s favor three times and this time he didn’t get the nod,” Mr. Dean said. Recalling his unsuccessful campaign for the presidential nomination in 2004, he added, “We all do what I did: When you lose, you pull behind the winner.”

Other Democrats, particularly Democrats in the Senate, were notably less aggressive in pushing Mr. Lieberman to leave. That reflected the fact that Mr. Lieberman is viewed as having a strong chance of winning the election in November; Democrats are looking to avoid doing anything now that might sour their relationships with Mr. Lieberman should he return to the Senate.

Several said they thought it was insensitive — and pointless — to call on him to quit now, saying that he might be more receptive to that argument later if polls show he is heading for what would be a second defeat. The dynamic could change if Republican officials succeed in persuading the party’s current Senate candidate, Alan Schlesinger, who got into the race at a time when Republicans thought they had no chance to unseat Mr. Lieberman, to step aside in favor of some better-known and better-financed Republican.

Republicans, who have been facing rough political waters, made little secret of the fact that they hoped to exploit the victory of an antiwar candidate in the Connecticut primary to portray the Democrats nationwide as weak on national security. Throughout the day, Republicans issued statements calling on Democratic challengers in some of the most contested elections to renounce Mr. Lamont.

“This is a defining moment in some ways for the Democratic Party,” said Tony Snow, the White House press secretary, in his opening remarks at the White House news briefing today. “I know a lot of people have tried to make this a referendum on the president; I would flip it. I think instead it’s a defining moment for the Democratic Party, whose national leaders now have made it clear that if you disagree with the extreme left in their party they’re going to come after you.”

In fact, the vast majority of Democratic Party leaders supported Mr. Lieberman in the primary and did not endorse Mr. Lamont until after the results were in.

Mr. Cheney offered warm praise for Mr. Lieberman, who was his opponent for vice president in 2000, though he said he did not want his remarks to be construed as endorsement of Mr. Lieberman. He cast Mr. Lieberman’s loss in ominous terms, suggesting that it would hearten American terrorist enemies.

Al Qaeda, he said, is “betting on the proposition that ultimately they can break the will of the American people in terms of our ability to stay in the fight and complete the task.”

“And when we see the Democratic Party reject one of its own, a man they selected to be their vice presidential nominee just a few short years ago, it would seem to say a lot about the state the party is in today,” he said.

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