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Tea Party leaders are condemning the rash of threats made against congressional lawmakers, saying violence and vandalism are not what they're about -- and that congressional Democrats are hardly the only ones dealing with intimidation over the health care debate.

The Tea Partiers say they've been enduring threats ever since their movement took off last year, and that while protesters were said to have shouted slurs at lawmakers on Capitol Hill over the weekend, other conservative protesters were harassed by counter-demonstrators. Virginia Rep. Eric Cantor, the Republican Whip in the House, also said Thursday that his campaign office in Richmond was shot at earlier in the week, though police said the bullet may have been randomly fired.

The Tea Party activists claim the latest threats aimed at lawmakers are, for the most part, coming from lone loons not associated with the Tea Party movement -- though at least one incident has been linked to Tea Party activists in Virginia. And they say they're concerned the intimidation could be used to smear those activists who are behaving responsibly.

"We support peaceful means," said Debbie Dooley, co-founder of the Atlanta Tea Party and a national coordinator for Tea Party Patriots, adding: "There are so many Tea Party groups that are out there. ... It's like herding cats. It's impossible."

Several Florida Tea Party groups released an open letter to Congress and President Obama Thursday night denouncing "all forms of violence."

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"We the leaders of the Tea Party movement of Florida stand in stark opposition to any person using derogatory characterizations, threats of violence or disparaging terms towards members of Congress or the President," they wrote.

Reports of new threats continue to emerge, after House Majority Leader Steny Hoyer announced Wednesday that more than 10 lawmakers have been harassed in some way. Cantor's announcement Thursday set off a flurry of finger-pointing, as members of both parties accused each other of trying to exploit the security concerns for political gain.

A senior Senate Democratic leadership aide told Fox News that there have also been threats made against Senate Parliamentarian Alan Frumin. Rep. Betsy Markey, D-Colo., has reportedly requested police patrols around her unoccupied home for fear it might be vandalized, after her office received a threatening message.

And, among other incidents, somebody cut a propane line attached to a grill at the Virginia home of Democratic Rep. Tom Perriello's brother. Tea Party activists had posted the address online, apparently believing it was the congressman's.

Mike Troxel, the blogger who posted the address online, told Fox News' Alan Colmes that he was encouraging voters to go to Perriello's house.

"I think people should have the right to have access to their, um, public officials," he said. When asked if the children of public officials should be harassed at their house just because they're related, Troxel said, "You know, I think that's a burden that comes with being an elected official."

But in the aftermath, both Republican and Democratic officials have condemned such behavior. And Tea Party leaders are being particularly vocal.

"I do not believe we should be encouraging people to visit homes because, although we disagree with their policies and their votes, they do have families," said Dooley, of the Atlanta Tea Party.

Some conservative activists are concerned leaders in Congress are trying to cast blame broadly.

House Majority Whip Jim Clyburn, D-S.C., in an interview with MSNBC Wednesday night, said people are getting "signals" from lawmakers on how to behave and that lawmakers need to "disown" the activity before it gets out of control. He suggested his colleagues were culpable.

"If we participate in it, either from the balcony or on the floor of the House, you are aiding and abetting this kind of terrorism, really," Clyburn said.

William Owens, a Tea Party activist from Nevada, said there's no getting around the fact that people are "provoked" because the government is "acting irresponsibly." But Owens said activists need to "be gentlemen" about their anger.

"I think most people are acting independently," he said. "I don't think you're going to find a credible Tea Party group condoning any of this activity."

Brendan Steinhauser, director of federal and state campaigns with the conservative group FreedomWorks, said he will be "reminding" activists to focus on "peaceful political efforts" and that any violence "will only set the movement back."

But he noted that his office received a bomb threat last September before a big protest in Washington, D.C.

"I think there is a double standard when it comes to covering how extremist elements on the left and the right behave," he said in an e-mail. "Both types of extremists should be condemned by the media and the rest of us who do not engage in such acts."