WASHINGTON (CNN) - House Democrats and Republicans participated in a rare bipartisan conference call Sunday to discuss the condition of Rep. Gabrielle Giffords as well as security concerns for members of Congress.
Republican and Democratic leaders, the chief of the United States Capitol Police, a doctor from the Office of the Attending Physician of Congress, and the Chief of Staff to Rep. Gabrielle Giffords briefed about 800 lawmakers, their spouses and top aides.
"I've been in Congress 22 years and I have never been on a conference call with Democratic and Republican leaders," Rep. Eliot Engel, D-New York, told CNN. He said he was struck by how genuinely bipartisan and impressive all the congressional leaders were who spoke - from Speaker John Boehner to Minority Leader Nancy Pelosi.
Washington state Democratic Rep. Adam Smith, who says he counts Giffords as his "closest friend" in the House, said the call was "to let people know how Gabby and the others were doing" and secondarily to discuss security concerns. "Obviously this is going to make us re-look at everything, but no specific recommendations came out of (the call)," Smith said.
Democratic and Republican aides on the call said House Sergeant-at-Arms Bill Livingood told members they need to be aware of their surroundings, designate a district staff member to deal with security issues and reach out to local law enforcement and U.S.Capitol Police if they have any safety concerns.
Sources say lawmakers will receive a more in-depth briefing Wednesday from Capitol Police, the sergeant-at-arms and the FBI.
Smith said only so much can be done. "We are public officials, we can't go out to every public meeting with six or seven armed guards around us," he told CNN.
But other lawmakers said they believe more dramatic security measures should be taken to help protect them, their families and their aides.
Rep. Jason Chaffetz, R-Utah, told CNN he has always has had a concealed weapon license and has often carried a weapon, which is legal in his state, but he said he "may do it more regularly now" in light of the attack on Giffords.
Chaffetz said he thinks Congress should consider using the U.S. Marshals Service, which protects federal judges, to provide security as needed for lawmakers when in their districts.
The U.S. Marshals Service is responsible for protecting the entire federal judiciary at their homes as well as their offices if necessary, following the attack on a Chicago judge's home in 2005.
Chaffetz said he is considering formally proposing the idea in his new role as chairman of the Homeland Defense Subcommittee of the Committee on Oversight.
Although he has only been in Congress two years, says he has already gotten half a dozen threats that have caused him to call the Capitol Police and local law enforcement for help.
He said U.S. marshals can be especially helpful at lawmakers' homes.
"I feel a vulnerability is my residence. It's so easy to figure out where a member of Congress lives," Chaffetz said.
"The violent tweets that you see out there, Facebook message boards, we're going to have to take these threats more seriously," he said.
Meanwhile, a Republican aide on the conference call said Boehner told members, "Gabby was attacked while doing the most important role of a member - listening. [Her aide] Gabe Zimmerman gave his life doing his job, helping his boss represent the people of his district."
Democratic and Republican leaders also announced they are working on a bipartisan resolution to bring to the House floor Wednesday to honor Giffords and other victims of the shooting rampage in Arizona.
House Majority Leader Eric Cantor sent a notice saying, "It is my recommendation that all Members of the House who can, return to Washington to honor those who have fallen and to receive any necessary security briefings from the U.S. Capitol Police."