WASHINGTON — After weeks of sometimes wrenching debate over gun safety, Congress will begin to consider legislation this week that is likely to include expanded background checks for gun buyers and increased penalties for those who purchase guns for criminals.

The best chance at legislative consensus appeared to rest in negotiations between Senator Charles E. Schumer, Democrat of New York, and Senator Tom Coburn, Republican of Oklahoma, over a measure they have yet to introduce that would expand background checks to nearly all gun purchases. Currently about 40 percent of gun purchases do not require them.

While Mr. Schumer and Mr. Coburn remain tantalizingly close, Senate aides say, their talks have stalled over a provision that would require records to be kept of private gun sales.

Republicans and many Democrats in Congress have historically opposed curbs on gun ownership, but public pressure to enact legislation has increased substantially since the Connecticut school shooting in December that left 20 children dead. Members of the Senate Judiciary Committee are likely to signal their intentions at a hearing on proposed gun legislation on Thursday, offering a preview of how other lawmakers might vote. The bill-writing process will probably continue into next week.