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In a rhetorical argument that is unlikely to yield any winners, Democratic lawmakers and their opponents in the health care debate have descended into a war of words over the symbols of Nazi Germany.

Town hall audiences and conservative bloggers protesting a Democratic-sponsored bill on health care reform have used the disturbing imagery to compare the plan championed by President Obama to how the Nazis treated prisoners in concentration camps.

Supporters have turned around and suggested the angry "mobs" are reminiscent of Adolf Hitler's blind followers. Some lawmakers say they have canceled public meetings because they fear for their lives.

But an axiom in political strategy states that whoever uses the Hitler comparison generally doesn't win the debate -- unless he's participating in a debate about Nazis.

Replacing a town hall meeting for a conference call in his district, Rep. Brian Baird, D-Wash., on Thursday compared his constituents' behavior to Nazi-era adherents.

"What we're seeing right now is close to Brown Shirt tactics," Baird told a local newspaper. "I mean that very seriously."

In an interview Wednesday, House Speaker Nancy Pelosi said of the protesters, "I think they are astroturf, you be the judge," using an expression that refers to orchestrated grassroots.

"They're carrying swastikas and symbols like that to a town meeting on health care," she said.

Ken Spain, a spokesman for the National Republican Congressional Committee, called such remarks evidence that Democrats are "desperate to climb their way out of message quicksand."

"Here's some free advice for the Democrats: When you are attacking the voters, you are losing," he said. "Conjuring up 'villains' and making elitist remarks about middle-class Americans isn't a strategy, it's a prayer."

A spokesman for Pelosi told FOXNews.com that the speaker was referencing a photo taken at a town hall meeting hosted by Rep. Ed Markey, D-Mass., which showed a protester holding a sign of a swastika crossed out over Obama's name and a question mark.

Another protestor at Rep. Lloyd Doggett's town hall meeting in Texas reportedly was seen with an SS symbol. Separately, one protester reportedly compared Massachusetts Rep. Jim McGovern to Josef Mengele, who conducted medical experiments on concentration camp prisoners.

At some events, protesters have been excessively boisterous in other ways. An image captured at Doggett's town hall showed someone holding a poster with devil's horns painted on the congressman's head. A Democratic National Committee Web ad contains an image of a constituent standing outside Rep. Frank Kratovil's office carrying a hanging effigy of the congressman.

Rep. Brad Miller, D-N.C., said he will not host any town halls this month because offices have received threatening phone calls, including one directed against his life. Instead, he will hold one-on-one meetings about health care reform with constituents.

Miller's office turned the death threat over to the Capitol Police.

"We are looking into the matter," Sgt. Jessica Baboulis, a spokeswoman for the U.S. Capitol Police, told FOXNews.com.

Acknowledging the health care debate across the country, U.S. Capitol Police Chief Terence Gainer issued a message on Thursday warning members not to overstate the threat, but to be aware of activity around them.

"There is no information known to us at this time indicating any criminal activity is being targeted toward any particular member or event. However, we do know that sometimes, tempers flare, with the potential for disruptions.

"Should that be the occasion, notifying local law enforcement authorities is highly recommended while attempts are made to calm the situation," reads the statement, which welcomes members to contact the police threat assessment division.

Aware of the possible downside of likening constituents to Nazis, Obama adviser David Axelrod met with Democratic Senate leaders on Thursday to review an action plan for the August recess.

He said while interest groups are organizing protests, he doesn't have a problem with that.

"I'm not going to disparage this. I believe in freedom of speech. I just think everybody ought to be able to talk," he said.

Senate Majority Whip Dick Durbin, who was in the meeting, said lawmakers aren't going to fall prey to efforts by "organized Web sites" like "Six Ways to Embarrass a Congressman" and "Right Time."

"We shouldn't fall for these sucker punches," Durbin said, admitting he is scaling back his town halls but not offering any details. "We can also spot a ringer."

"We're not going to be sabotaged," added Senate Majority Leader Harry Reid. "We're heading home with our heads held high, because we have done good work here."