(CNN) – The Senate Judiciary Committee could begin considering gun control bills as soon as Thursday, including a measure that would ban military-style assault weapons.
Other pieces of legislation that will be considered by the panel are measures stopping illegal trafficking of guns, bolstering background checks on gun sales, and improving security in schools. Republicans could force a postponement of the Senate panel's mark up of gun legislation for one week.
Of the proposed bills, background checks are considered the most likely to gain Congressional approval. The assault weapons ban, which was introduced by Democratic Sen. Dianne Feinstein of California, is opposed by Republicans and some pro-gun Democrats.
President Barack Obama pressed Congress to pass tighter restrictions on guns in the aftermath of December's deadly shooting at an elementary school in Connecticut. The four bills up for consideration by the Senate Judiciary Committee have all been supported by the president.
On Sunday, Republican Sen. Tom Coburn of Oklahoma, who is among a bipartisan group of four senators working behind the scenes on a bill to expand background checks, said a sticking point had emerged on whether to keep records on gun owners.
"I don't think we're that close to a deal," the Oklahoma Republican said on "Fox News Sunday." "There absolutely will not be record-keeping on legitimate, law-abiding gun owners in this country. If they want to eliminate the benefits of actually trying to prevent the sales to people who are mentally ill and to criminals, all they have to do is to create a record-keeping. That will kill this bill."
Coburn, who maintains an A rating with the National Rifle Association, is joined in his group by Sen. Mark Kirk, R-Illinois; Sen. Joe Manchin, D-West Virginia, a longtime advocate of gun rights; and Chuck Schumer, D-New York, a longtime supporter of gun control.
The chairman of the Senate Judiciary Committee, Sen. Patrick Leahy of Vermont, was adamant Sunday that expanded background checks would not include provisions to register gun owners, but he said that responsible Americans looking to purchase firearms shouldn't fear robust checks.
"They check to see if you told the truth, and then it's cleared out," Leahy said of the current background check system, adding later that measures to register gun owners would not be part of Senate gun control legislation.
"It's not going to be registration," he said on CNN's "State of the Union," adding that Republicans and gun advocates need to "lower the rhetoric and talk reality."