* Democratic-led panel expected to back four bills
* But unclear which if any of them will win Senate approval
* Dispute arises over background checks for gun owners
By Thomas Ferraro
WASHINGTON, March 7 (Reuters) - Less than three months after the Connecticut school shooting, a campaign to tighten U.S. gun laws that is backed by President Barack Obama will go to its first votes in Congress on Thursday when a U.S. Senate panel meets.
The Democrat-controlled Senate Judiciary Committee is expected to approve the four bills that make up the gun-control package in voting over the next day or so.
That will sets up fights in the full Senate over a proposed ban on assault weapons and a plan to expand background checks on prospective gun buyers.
Wider background checks had been seen as one of the measures with most chance of success in Congress, but the push for this it has stumbled in recent days over a dispute about whether to keep records of private gun sales. Republicans fear such records would be a first step to a government register of gun owners.
Republican Senator Tom Coburn of Oklahoma said it was possible to reach an agreement with Democrats on background checks but there was a chance "we won't, and that will be a shame."
The drive for gun-control laws has taken on a new urgency since the December shooting in which a gunman killed 20 children and six adults at a school in Newtown, Connecticut.
It has become one of Obama's top domestic priorities, along with immigration reform and fixing a series of budget messes.
But reviving an assault-weapons ban that ran out in 2004 has almost no chance in Congress due to opposition from Republicans and even some Democrats.
The two parties are closer to agreement on the two lesser elements of the gun-control drive: cracking down on the illegal trafficking of firearms and bolstering school security.
The chairman of the Senate Judiciary Committee, Vermont Democrat Patrick Leahy, increased the chances of his bill to combat unlawful gun trafficking when he attracted four co-sponsors on Monday - two fellow Democrats and two Republicans.
The panel's top Republican, Senator Charles Grassley, said he might also join them in backing the bill, which would toughen statutes against "straw purchasers" - people who profit from buying guns then selling them to those prohibited from owning firearms.
"The practice of straw purchasing is used for one thing - to put firearms into the hands of those that are prohibited by law from having them. Many are then used to further violent crimes," Leahy said on Tuesday.
Democratic Senator Barbara Boxer has received bipartisan support for her bill to provide $40 million a year for 10 years in matching federal grants to schools to strengthen security.
The measure would authorize the U.S. Justice Department to create a National Center for Campus Public Safety to serve as a clearing house for best practices and information.
"Congress spends hundreds of millions a year to protect its members. It can certainly spend $40 million a year to protect our children," the California senator said on Monday.
Democrats control the Judiciary Committee 10-8 but they might need 60 votes to clear gun control legislation in the 100-member Senate where they have only a 55-45 majority. (Editing by Alistair Bell; Editing by David Brunnstrom)