Washington - Connecticut's two senators took to the Senate floor Tuesday to call for a ban on assault weapons.

"I'd support a restoration of the assault ban today," said Sen. Joseph Lieberman, D-Conn. "These are weapons that were developed by our military originally, not by private industry for hunting or sports shooting purposes. They shouldn't be sold."

Sen. Richard Blumenthal, D-Conn., said that these weapons "are not designed for self-defense or hunting, but rather for killing as many people as possible, as fast as possible. There is no reason that such weapons should be for sale in America today."

U.S. Rep. Chris Murphy, D-Conn., said the tragedy in Newtown, which is in his district, will change his priorities when he succeeds the retiring Lieberman next month.

"My number one job now is to make sure this nation learns lessons about what happened in Newtown," he said.

"I'm going to show up in the Senate as the voice of those 20 kids and those six brave adults," said Murphy, referring to the 26 people killed at Sandy Hook Elementary School.

An assault weapons ban was enacted by Congress in 1994 during the Clinton administration, when Congress was under Democratic control. It expired in 2004, and was not renewed by a Congress dominated by the Republicans. The Obama administration is said to be giving consideration to seeking such a ban when the 113th Congress convenes in January.

While acknowledging there is no one solution to the problem of mass violence, Murphy said the answer "clearly starts with getting these awful weapons out of the hands of people who don't need them."

He also said it was important to bring mental health and developmental disorders "out of the shadows" and examine what he calls a "culture of violence."

Both Blumenthal and Lieberman also support increased background checks for those purchasing a gun - including those not sold by licensed dealers, such as those sold at gun shows. Lieberman noted that terrorists have managed to buy weapons at gun shows.

"I've talked to people since Friday who have said to me, 'Why will this be any different? Nothing happened after Columbine or Aurora or Virginia Tech or any of the other acts of mass violence in our society,'" said Lieberman, noting that he didn't blame people for being skeptical. But he continued: "I see signs of hopes around us. Colleagues who have been protectors of gun rights saying in the last few days, 'This has got to change. We've got to come together and reason together and act together, and everything has to be on the table, including our gun laws.'"

Blumenthal also called for a ban on high-capacity magazines, saying that "neither hunting nor self-defense requires 30-round clips."

Rep. Joe Courtney, D-2nd District, said Tuesday that he also supports a ban on assault weapons and high-capacity magazines. He noted that in the landmark Supreme Court case District of Columbia v. Heller, which interpreted the Second Amendment's right to bear arms as applying to individuals, conservative Justice Antonin Scalia acknowledge that this right could be abridged.

"If you read the decision, he clearly states that that does not mean any person has the right to have any firearm under any circumstances," Courtney said in an interview. "So if you look at the boundaries that the godfather of conservative legal philosophy in America put out there, the fact is that we have room here to make some changes."

Blumenthal, for one, seemed determined to make some changes.

"I will work to find a solution to this crisis - because it is a crisis - and I will not be deterred by any organization or campaign that uses scare tactics or intimidation," he said Tuesday morning. "Because there was nothing more frightening than looking into the eyes of the parents who lost their children last Friday - that is any parent's worst nightmare."