(CNN) -- Lawmakers on Sunday called for toning down the political rhetoric in Washington and across the country following a deadly shooting in Arizona that left six people dead and left a congresswoman with a bullet wound to the brain.

"We live in a world of violent images and violent words, but those of us in public life and the journalists who cover us should be thoughtful in response to this and try to bring down the rhetoric which I'm afraid has become pervasive in our discussion of political issues," Sen. Dick Durbin, D-Illinois, told CNN's "State of the Union."

The comments came a day after Arizona Rep. Gabrielle Giffords was shot, along with 19 others, by a man outside of a supermarket in Tucson. Six people died, authorities said, and suspect Jared Lee Loughner was taken into custody by police.

Sen. Lamar Alexander, R-Tennessee, told CNN, "We have to be very careful about imputing the motives or the actions of a deranged individual to any particular group of Americans who have their own political beliefs." He added, "We ought to cool it, tone it down, treat each other with great respect, respect each other's ideas and even on difficult issues like immigration or taxes or health care law, do our best not to inflame passions."

Other lawmakers from both sides of the aisle echoed those comments across the Sunday political talk shows. Their message: While the motivation of the gunman remains unknown, it is time to dial back the fury that has overtaken so much of the U.S. political discourse.

"This ought to be a wake-up call to not only the members of Congress but to the people of this country that we are headed in the wrong direction," said Rep. Emanuel Cleaver, D-Missouri, on NBC's "Meet the Press." "Congress meets a lot but it rarely comes together."

He added, "We've got to watch what we say, and we're not doing it. It starts in campaigns."

Rep. Steny Hoyer, D-Maryland, told CBS' "Face the Nation" that he had spoken with Giffords' husband, Mark Kelly, who is "very angry about the level of angry rhetoric that he believes incites people."

Officials in Arizona voiced dismay over the possibility that highly polarized rhetoric in the conservative hotbed state may have played a role in the assassination attempt of Giffords, who was targeted during a meet-and-greet with constituents in a shopping center. A federal judge, a 9-year-old girl, and four other people died in the mass killing.

While not stating a motive for the shootings, Pima County Sheriff Clarence Dupnik in Tucson used a nationally televised press conference to condemn the tone of political discourse in his state. He charged that public debate is now "vitriolic rhetoric" which has rendered Arizona "the mecca for prejudice and bigotry."

Dupnik suggested that such rhetoric can have deadly consequences.

"We need to do some soul searching," Dupnik told reporters. "It's the vitriolic rhetoric that we hear day in and day out from people in the radio business and some people in the TV business.

"When you look at unbalanced people, how they respond to the vitriol that comes out of certain mouths about tearing down the government, the anger, the hatred, the bigotry that goes on in this county is getting to be outrageous. Unfortunately, Arizona, I think, has become sort of the capital," Dupnik, a Democrat, continued.

"We have become the mecca for prejudice and bigotry," he said.

Arizona is a Republican stronghold where the party members hold a two-thirds majority in both chambers of the legislature and occupy the governor's office.

"People who are unbalanced may be especially susceptible to vitriol," Dupnik said. "It's not unusual for all public officials to get threatened constantly, myself included. That's the sad thing that's going on in America. Pretty soon we're not going to be able to find reasonable people to subject themselves to serving the public."

Dupnik added, "People tend to pooh-pooh this business about the vitriol that inflames American public opinion by the people who make a living off of that. That may be free speech but it's not without consequences."

Last March, Giffords raised concerns about inflammatory rhetoric after her office was vandalized, and she cited that her name appeared on a website titled "take back the 20" as part of a list originally issued by Sarah Palin against vulnerable House Democrats.

A map on the site showed crosshairs over the contested Democratic districts.

Palin first posted the list in March 2010, naming 20 House members who voted for health care reform and represented districts that Republican Sen. John McCain of Arizona won in the 2008 presidential election.

At the time, Giffords responded to the map by saying on MSNBC that her long-serving colleagues had "never seen anything like it."

"The thing is, the way that she has it depicted has the crosshairs of a gun sight over our district," Giffords said in March. "When people do that, they've got to realize there's consequences to that action."

Palin once famously tweeted, "Commonsense Conservatives & lovers of America: 'Don't Retreat, Instead - RELOAD!'" But she emphasized that she was not encouraging violence, rather just encouraging conservatives to fight for their positions.

On Saturday, Palin posted a message on her Facebook page: "My sincere condolences are offered to the family of Rep. Gabrielle Giffords and the other victims of today's tragic shootings in Arizona. On behalf of Todd and my family, we all pray for the victims and their families, and for peace and justice."

Durbin, speaking Sunday to CNN, said, "The phrase 'don't retreat, reload,' putting crosshairs on congressional districts as targets -- these sorts of things, I think, invite the kind of toxic rhetoric that can lead unstable people to believe this is an acceptable response."

He said he was not drawing a direct connection between the shooting and Palin's remarks, or those of anyone. "But don't we have an obligation... to say this is beyond the bounds?"

On "Fox News Sunday," Rep. Cathy McMorris Rodgers, R-Washington, said, "Without a doubt, the political rhetoric has increased across the board, inflammatory remarks. And Republicans, Democrats, liberals, conservatives, Tea Party activists have all condemned what happened in Arizona. I think it's important to remember that this was an individual 22 years old, he dropped out of high school. As far as we know, he's not tied to a political movement, and this wasn't a politically motivated act."

Tom Fuentes, a former FBI assistant director who's a CNN contributor, said that when media cover "hateful" public statements by officials or television personalities, those remarks are often framed as "they're exciting their base," Fuentes said.

"Law enforcement executives out there know, like this sheriff, that it also excites the lunatic fringe," Fuentes told CNN. "In this country, we have no shortage of mentally unbalanced people, and it seems in case after case, they have no trouble obtaining firearms. So when they go over the edge and go public and try to initiate an attack, this is what happens."

Arizona state Rep. Matt Heinz, a Democrat and a Tucson physician, supported Dupnik's remarks.

"I think he is very, very correctly calling attention to some of the vitriol and some of the ways we're talking about each other," Heinz told CNN. "For those with troubled minds, sometimes some of those things that are said are unfortunately taken in the wrong way."

Arizona state Rep. Steve Farley, a Democrat from Tucson, said the country now faces a challenge of overcoming polarizing politics. His political aide witnessed the shootings and applied pressure to Giffords' wounds, he said.

"The question is, can we come together as a state and can we come together as a country and sort of put this harsh hyper-rhetoric that has caused people who are a little unhinged in the first place to go over the edge," Farley told CNN.

"This country is something that deserves no less than a politics that rises above violence," he added.

McCain, the state's Republican senator, said he was "horrified by the violent attack on Representative Gabrielle Giffords and many other innocent people by a wicked person who has no sense of justice or compassion. ... Whoever did this, whatever their reason, they are a disgrace to Arizona, this country and the human race, and they deserve and will receive the contempt of all decent people and the strongest punishment of the law."

House Speaker John Boehner, R-Ohio, was among the many other lawmakers on both sides of the aisle who quickly condemned the shooting. "An attack on one who serves is an attack on all who serve. Acts and threats of violence against public officials have no place in our society," he said.

Former U.S. Rep. John Boccieri, a Democrat from Ohio, was threatened last year when a man said he would burn down Boccieri's house. The man is facing jail time.

That threat came amid "the heat of the debate over the health care issue," Boccieri told CNN Sunday. "Intimidation and threats of violence have no realm in our public discourse. We should make sure that we hold folks accountable like that and prosecute them to the fullest extent of the law."

In the wake of the shooting in Arizona, Boccieri said, "I would hope that our country would appeal to its better senses so we could tone down the heated rhetoric and discuss with a degree of civility these important concepts and issues."

He added, "Both sides, in my opinion, are guilty of this and we know that folks are struggling, they're at last end's rope in some instances, and some of this rhetoric could push folks over the top."

But Boccieri also warned against deciding too soon what may have fueled the Arizona shooter, since the facts of the case are still being investigated.

The U.S. House of Representatives agreed Saturday that it will cease any discussion next week about repealing President Barack Obama's health care reforms -- a law opposed by many Arizona Republicans and voters in a November ballot measure -- and instead address Saturday's shootings.

Tea Party Express Chairman Amy Kremer said she was saddened by the mass shooting.

"These heinous crimes have no place in America, and they are especially grievous when committed against our elected officials," Kremer said. "Spirited debate is desirable in our country, but it only should be the clash of ideas. An attack on anyone for political purposes, if that was a factor in this shooting, is an attack on the democratic process. We join with everyone in vociferously condemning it."

CNN's Michael Martinez, John Helton and KC Wildmoon contributed to this story.