Early last week, a distressing, if not entirely unsurprising, Newsweek poll found that fully 40 percent of American adults continue to believe that Iraq was directly involved in the 9/11 attacks.

It must, then, have been this exasperating chunk of the electorate that Joe Lieberman had in mind when he declared Sunday on ABC’s “This Week” that Democrats are doomed in the 2008 presidential race unless they re-embrace the Iraq War.

“I think that’s the best tradition of our party, and if we don’t recapture it ... the Democratic candidate is going to have a hard time winning that election next year,” Mr. Lieberman said, likening his own hawkish Iraq posture to Harry Truman, John F. Kennedy, Hubert Humphrey, and Henry “Scoop” Jackson – all of them much too deceased to protest such a questionable comparison.

And if losing to the Republicans isn’t enough, Mr. Lieberman also made clear that any Democratic nominee who favors “retreat” risks losing his personal endorsement. After offering praise for Republicans John McCain and Rudy Giuliani for showing independence from their party’s base (and conveniently ignoring the abuse Ron Paul has suffered from the G.O.P. establishment for his war opposition), Connecticut’s junior Senator told ABC’s George Stephanopoulos: “It does seem to me now that the leading Democratic candidates for President are competing with each other to see which one can more quickly pull more of our troops out of Iraq, while our troops are there fighting and now succeeding with a lot on the line for the future security of the United States of America.”

In truth, the front-running Democratic candidates, all of whom favor a withdrawal of American troops from Iraq, are doing just fine ignoring Mr. Lieberman’s electoral prescription. Hillary Clinton, Barack Obama and John Edwards all generally hold leads over the most likely Republican nominees. Moreover, surveys show that voters lopsidedly prefer a generic, unnamed Democrat to an unnamed Republican for President. With President Bush’s approval ratings in the toilet, thanks almost entirely to Iraq, the next election is the Democrats’ to lose.

In all, Mr. Lieberman’s “This Week” appearance lasted about 11 minutes, and if anything became clear in that time it’s that his influence over the national political debate is waning – a decline that not many foresaw last November, when Connecticut’s voters returned him to the Senate, prompting talk that a new power-broker, coveted equally by both parties, had been born.

Given the Senate’s partisan balance – 49 Republicans, 49 Democrats (one still recuperating from a December cerebral hemorrhage), and two tie-breaking independents who caucus with the Democrats – Democrats are still technically at Mr. Lieberman’s mercy, their fragile control of the chamber dependent on his continued willingness to live up to his campaign pledge to side with his old party for organizational purposes.

But it’s now apparent that they need nothing more than that from him. Republicans have labored to portray Mr. Lieberman’s defeat in last year’s Senate primary as evidence that the Democratic Party has been over-run by weak-willed McGoverniks, a contention that Mr. Lieberman, in making reference to Democrats’ past vulnerabilities on foreign policy and national security issues, sought to reinforce on Sunday.

That game, however, has ceased to work. In years past – 2004 and 2002, say – a public association with Mr. Lieberman was helpful to Democrats, a reassurance to a more hawkish electorate that they were as “tough” as the G.O.P. But in 2007, embracing Mr. Lieberman’s intransigence is a decided political liability – evidenced most startlingly by a recent poll that found that even 58 percent of Republicans in Iowa want a troop withdrawal in the next six months. When, as he did on Sunday, Mr. Lieberman uses a national television interview to dust off old attacks on the Democratic Party’s foreign policy credentials while at the same time actually declaring that “the surge is working,” it only benefits his former party’s standing with the war-wary public. There are few, if any Democrats, quaking at his threat to endorse a Republican in ’08.

Similarly, his prospective defection to the Senate G.O.P. seems less likely now – again because of Iraq. One after another, the Senate’s moderate Republicans are now making a break from the Iraq policy championed by the Bush administration and Mr. Lieberman. By September, it seems more and more likely, the President will either take the hint and reduce troop levels or watch as those fed up Republicans side with the Democrats to impose a withdrawal timetable. Indeed, Mr. Lieberman’s interview was preceded with a clip of Senator Richard Lugar’s time-to-junk-the surge floor speech last week. If Mr. Lieberman were to flip to the Senate G.O.P. now, he’d probably still be surrounded by colleagues intent on ending the war.

There was actually a moment, in the aftermath of the 2006 elections, in which his triumph was the rare exception to a profoundly anti-war national tide, when a remarkable redemption story actually seemed possible for Mr. Lieberman, the Democratic vice-presidential nominee in 2000. However foolishly, it was believed back then that President Bush would respond to the election results – and the report of the Iraq Study Group report – with a rethinking and scale-back of the war, which might have significantly deflated the issue’s primacy in the ’08 race. Had Mr. Bush done so, Mr. McCain may well have sustained his front-runnerhood on the G.O.P. side – raising the possibility that as the nominee he’d offer his Number Two slot to his friend Mr. Lieberman, capitalizing on the cross-party appeal of someone known primarily for his political independence.

But Mr. Bush dug his heels in and Mr. McCain and Mr. Lieberman cheered him on, and now both of them are identified almost exclusively with the unpopular war (with a little immigration thrown in for Mr. McCain). Now, as he drops to single digits in Republican polls, it seems ludicrous to imagine Mr. McCain as the ’08 G.O.P. nominee, and inconceivable that he’d round out his ticket with someone so intimately attached to such an unpopular war. Not very long ago, both men had enviable reputations as courageous political mavericks; in a few short months, they have become bullheaded apologists for a policy that has fallen into deep disfavor with the public.

In discussing the melting Congressional support for the war, Mr. Lieberman said on Sunday that “You might say that in Iraq we’ve got the enemy on the run, but for some reason in Washington a lot of politicians are on the run to order a retreat by our troops even as they are beginning to succeed.”

Those politicians are on the run to catch up with the public before November 2008. Mr. Lieberman should probably consider himself lucky that his seat was up last year – and not next year.