These officials say the two sides are discussing a plan to raise the debt limit by about $2.4 trillion and enact spending cuts of a slightly larger amount in two stages.
The deal under discussion would also require Congress to vote on a balanced budget amendment to the Constitution, but not require its approval.
The officials spoke on condition of anonymity, citing the sensitivity of the discussions.
On Saturday, as the Associated Press reported, Senate Majority Leader Harry Reid said there was no deal to break the debt impasse in Congress and that no weekend progress had been made as a default deadline approaches.
Reid made his comments on the Senate floor after the Republican leader, Sen. Mitch McConnell of Kentucky, said he was confident a deal would be reached. Democrat Reid said the Republicans "still refuse to negotiate in good faith."
McConnell on Saturday listened to Reid's remarks and then responded that he was more optimistic about the outcome. Said McConnell: "I think we've got a chance of getting there."