In the wake of a mass shooting in Arizona that left six dead and one congresswoman in the hospital, some Republican lawmakers seem to be most worried about finding ways to protect themselves.

Rep. Dan Burton (R-IN) wants to enclose the House Gallery in "a transparent and substantial material" such as Plexiglas, an aide told CBS News.

His legislation aims to keep the public from being able to throw explosives or other materials at members while they are on the House floor.

It's not the first time Burton has proposed such a measure. An earlier bill reads, "The Architect of the Capitol shall enclose the visitors' galleries of the House of Representatives with a transparent and substantial material, and shall install equipment so that the proceedings on the floor of the House of Representatives will be clearly audible in the galleries."

The bill cites past attacks on Congress, including a 1915 bombing by an anti-war protester, the shooting of five members of Congress during a vote in 1954, and a 1971 bomb placed in the Senate bathroom by the Weather Underground. It's not clear how the proposed legislation would have made a difference in the case of the Weather Underground bomb.

Another GOP congressman, Rep. Peter King of New York, is advancing a bill that would make it a crime to bring a firearm within 1,000 feet of a government official.

New York Mayor Michael Bloomberg released a statement Tuesday backing the measure.

"In the United States, it is illegal to bring a gun within 1,000 feet of a school," the statement said. "Passing a similar law for government officials would give federal, state, and local law enforcement a better chance to intercept would-be shooters before they pull the trigger."

Democrats are also planning their own legislation in reaction to the shootings.

Sen. Frank Lautenberg (D-NJ) and Rep. Carolyn McCarthy (D-NY), two of the most outspoken gun control advocates in Congress, were also sponsoring legislation that would restrict high-capacity ammunition clips like the one used Saturday.

"The only reason to have 33 bullets loaded in a handgun is to kill a lot of people very quickly," Lautenberg said in a statement. "These high-capacity clips simply should not be on the market. Before 2004, these ammunition clips were banned, and they must be banned again."

Rep. Jesse Jackson Jr. (D-IL) has proposed increasing lawmakers' budgets by 10 percent to pay for extra security in district offices.

"I will propose a 10 percent increase in member budgets for security measures," he said. "In some districts, that will mean hiring security personnel for public events. In other areas, that may mean installing surveillance cameras at district offices as a deterrent or improving the locks or the entry systems in district offices. Some will need more resources in order to move their offices to a safer area."

"I do not feel that fear should grip us, but since 9/11 we've secured every federal facility with the exception of our district offices. After the events of last weekend it is clear that our district staffs are vulnerable. Members should have the resources and the latitude to take the appropriate security measures in order to protect themselves and their staffs," Jackson added.

The legislation would also restore a five percent cut in House member budgets enacted by Republicans last week.

-- With earlier reporting by Sahil Kapur