ATLANTA (CNN) -- Voters turned out to pick nominees in two closely watched Democratic congressional races Tuesday, with polls showing Sen. Joseph Lieberman in Connecticut and Rep. Cynthia McKinney in Georgia trailing upstart challengers.
Lieberman, who was former Vice President Al Gore's running mate in 2000, is seeking the Democratic nod for a fourth Senate term. He faces cable-television executive Ned Lamont, a former Greenwich city councilman running his first statewide campaign.
Meanwhile, McKinney -- a vehement critic of President Bush who recently avoided charges in a March scuffle with a Capitol Police officer -- is seeking to hold her seat in a runoff against Hank Johnson, a former county commissioner in her suburban Atlanta district.
Primaries are also taking place in Colorado, Michigan and Missouri, but the Democratic race in Connecticut is the most closely watched of Tuesday's races.
Lieberman was an unsuccessful contender for the Democratic presidential nod in 2004. He has been blasted by many Democrats in Connecticut and nationwide not only for his outspoken support of the war in Iraq, but also for his criticism of fellow Democrats who disagree. (Watch Lieberman's fans and foes among the voters -- 1:36)
"I think too often, Sen. Lieberman goes out of his way to undermine the Democratic message," Lamont said Monday.
In a state President Bush lost by a 10-point spread in 2004, Lieberman's critics have crystallized their complaint in a single image: Bush's embrace of Lieberman before the 2005 State of the Union address. Lamont boosters have mocked the scene with a pickup-mounted replica of the scene, dubbed "The Kiss."
Lieberman calls accusations that he has been a "cheerleader" for Bush "ridiculous." Former President Bill Clinton, former Georgia Sen. Max Cleland and fellow Connecticut Sen. Chris Dodd have campaigned for him in recent weeks.
"I have opposed most of what this president has asked us to do in Congress," he said. "And secondly, that somehow I am not a real Democrat? It is outrageous."
Lieberman trailed Lamont by 6 percentage points in a Quinnipiac University poll out Monday -- about half the spread he faced the previous week.
However, despite the recent polling, Lieberman told campaign supporters that he expects to be the winner at the end of the evening.
"I gotta tell you, I have a very good feeling as we begin this primary day," Lieberman said. "This primary is not a referendum on George Bush. This is a choice they have between their senator, Joe Lieberman, and a guy coming up without any experience, running on one issue and running a negative campaign."
Despite Lieberman's expressed confidence, he has also threatened to run as an independent in November's election if he fails to claim the party's nomination, further enraging party activists and many Web commentators, who have boosted Lamont.
On Tuesday afternoon, Lieberman campaign accused Lamont's of "dirty politics" on Tuesday after a denial-of-service attack knocked out the Lieberman campaign Web site. Lieberman spokesman Sean Smith compared the hack to the kind of tactics used by Karl Rove, Bush's top political adviser. (Full Story)
"There is no place for these Rovian tactics in Democratic politics, and we demand that our opponent calls off his supporters and their online attack dogs," Smith said.
The Lamont campaign denied involvement with the hacking. "We urge whoever did it to stop," Lamont spokeswoman Liz Dupont-Diehl said.
"We don't know who is doing it," she said. "Ned has always been very clear that he doesn't encourage or tolerate behavior like this."
McKinney trails challenger
Meanwhile, McKinney appeared to face an uphill battle in Georgia's 4th Congressional District, a largely African-American district she has represented for most of the past 14 years. Published polls showed her trailing Johnson, who has called her "an embarrassment" to the district.
McKinney, an outspoken liberal, calls herself Bush's "worst nightmare." She lost her bid for a sixth term in Congress in 2002, after she suggested that members of the Bush administration stood to profit from the war that followed the September 11, 2001, attacks on New York and Washington -- but won the seat back in 2004.
In March, she clashed with a Capitol Police officer who stopped her to check her credentials. She announced later that she was sorry for what happened, and a District of Columbia grand jury that looked into the matter brought no charges. But she's still defending herself.
"The fact of the matter is, I was never charged with anything," she said in one of her debates with Johnson.
She fell short of a win in a three-way race in July's Democratic congressional primary, leading Johnson 47 percent to 44 percent. Johnson said her scuffle with the police was "one more controversy that could have been avoided."
He says he's running on the "ABC" ticket -- "Anybody but Cynthia" -- and promises to be a less divisive figure if elected.