Senators could start debating Democratic-written gun legislation before week's end. But leaders also might decide to give negotiators more time to seek a deal on expanding background checks for firearms buyers.
Passing the expanded background checks would be viewed as a victory for gun-control advocates after Democratic leaders made it clear that supporters were nowhere close to getting a majority of votes in favor of reinstituting an assault weapons ban.
Both measures have been a priority for President Barack Obama since the Dec. 14 shooting at an elementary school in Newtown, Conn. On Monday Obama travels to Connecticut to again make the case for gun legislation, with a speech at the University of Hartford.
"He's been working with both sides to try to get the strongest bill we can that has enforceable background checks," White House senior adviser Dan Pfeiffer said Sunday on ABC's "This Week."
The National Rifle Association opposes both the assault weapons ban and the expanded background checks.
Short of unanimous support in their own party, Democratic senators have been unable to strike a deal with Republicans for the votes they would need to push background check legislation through the chamber. Senate Majority Leader Harry Reid, D-Nev., might delay debate to give bargainers more time, underscoring how crucial the proposal is to the gun control drive.
"If we go to the floor, I'm still hopeful that what I call the sweet spot -- background checks -- can succeed," Sen. Chuck Schumer, D-N.Y., said Sunday, referring to the start of debate by the full Senate. "We're working hard there."
Dan Gross, president of the Brady Campaign to Prevent Gun Violence, called the measure "the most pivotal piece" of Democrats' gun legislation.
Also high on Congress' agenda is immigration, where a decisive moment is approaching.
Bipartisan groups in the House and Senate are expected to present legislation as early as this week aimed at securing the U.S. border, fixing legal immigration and granting legal status to millions who are in the United States without authorization. That will open months of debate on the politically combustible issue, with votes by the Senate Judiciary Committee expected later this month.
The House is looking at a busy, if more low-profile agenda in the coming weeks.
In its first week back, the House will consider a bill that would prevent the National Labor Relations Board from issuing rules until a dispute over administration appointees is resolved.
Among the bills that could see action in later weeks is a measure requiring the Treasury to pay principle and interest on debt held by the public if the nation's borrowing limit is reached but not extended.
Other measures would prioritize pediatric research to assist children with autism and give workers greater flexibility to choose paid time off instead of overtime pay.
Lawmakers will devote much time to the 2014 budget proposal that Obama plans to release on Wednesday. It calls for both new tax increases, which Republicans oppose, and smaller annual increases in Social Security and other government benefit programs, over the objections of many of the president's fellow Democrats.
Even with a background check deal, Senate debate on gun legislation may begin at a slow crawl with some conservatives promising delays and forced procedural votes. Sen. John McCain, R-Ariz., on Sunday urged fellow Republicans to allow debate to go forward, even as he declined to express support for a background check bill.
"I don't understand it. The purpose of the United States Senate is to debate and to vote and to let the people know where we stand," McCain said, appearing alongside Schumer on CBS' "Face the Nation."
There's a strong chance the first votes won't occur until at least mid-April.
Until Democrats come out with the final shape of their background check measure, gun control advocates nervously are tracking the private negotiations, worried their allies might cut a deal that goes too far.
"We want a vote on the issues, we don't want them watered down so they're unrecognizable," said Joshua Horwitz, executive director of the Coalition to Stop Gun Violence. "If they can't vote for it, let the American people judge them on that. Don't let a dumbed-down bill be the outcome of this."
The Senate gun legislation would toughen federal laws against illegal firearms sales, including against straw purchasers, or those who buy firearms for criminals or others barred from owning them. The legislation also would provide $40 million a year, a modest increase from current levels of $30 million, for a federal program that helps schools take safety measures such as reinforcing classroom doors.
Omitted from the bill are bans on assault weapons and high capacity ammunition magazines, both factors in the shooting at Sandy Hook Elementary School. Those bans were approved last month by the Senate Judiciary panel. Reid has said he will allow both to be offered as amendments by their sponsor, Sen. Dianne Feinstein, D-Calif., but neither seems likely to survive.
Many experts agree that the proposal with the widest potential reach is a broadening of background checks, now required only for transactions by the roughly 55,000 federally licensed firearms dealers. Proponents want to cover private sales, such as those between individuals at gun shows or online.
One major hang-up has been Democrats' insistence on retaining records of private sales, which they say is the best way to ensure background checks are actually conducted. Sen. Tom Coburn, R-Okla., a leader of conservatives in the talks, has rejected that as excessive government intrusiveness.
The system is aimed at preventing guns from going to criminals, people with severe mental problems, some drug abusers and others.
The National Rifle Association and other critics say the checks are ignored by criminals, and they fear that expanding the system could be a prelude to the government maintaining files on gun owners. Current law forbids that. The government must destroy records of the checks within a day, though gun dealers must retain information on the transactions for 20 years.
"We remain committed in our opposition to expanding a broken system," said NRA lobbyist Chris W. Cox.
Justice Department figures show that from 1994 when the system began through 2010, 118 million would-be gun buyers were checked and 2.1 million were denied firearms. Defenders say the data proves the checks prevent many dangerous people from getting weapons.
The current background check measure, by Schumer, would expand the system to cover nearly all gun transactions, with narrow exceptions that include sales involving immediate relatives such as parents and children. Even without a bipartisan deal, Schumer is expected to expand the exemptions to more relatives, people with permits to carry concealed weapons and others.
Schumer and Sens. Joe Manchin, D-W.Va., and Mark Kirk, R-Ill., have been shopping alternatives in an effort for more GOP support. Democrats are sure to need 60 votes in the 100-member chamber to win, but there are just 53 Democratic senators plus two Democratic-leaning independents.
Democrats have considered requiring background checks for all gun show and online sales, but exempt face-to-face transactions between private individuals who do not run commercial gun enterprises.
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