President Bush has demanded immediate congressional action after months of delay.
"We hope by Tuesday or Wednesday we could have a bill that would be passed by the Senate by a wide margin," said Sen. Trent Lott, R-Miss., adding that negotiators worked over the weekend on a deal. "It would be different than probably either side proposed earlier."
The Senate's top Democrat, Tom Daschle of South Dakota, said he also believes a compromise can be reached. He said he would provide one of the 60 votes needed to stop a filibuster if one develops.
"We are going to try to get this done," said Daschle, who appeared with Lott on NBC's "Meet the Press."
One question is whether Lott or Daschle, the current majority leader, will run the Senate during the session that starts Tuesday. That depends on who wins the vote of an independent temporarily named to the seat of late Sen. Paul Wellstone, D-Minn. Appointee Dean Barkley has not said what he will do.
Daschle and Lott did not say what shape they expect a compromise to take. A dispute over workers' rights has held up the legislation in the past. Bush has insisted that the department's workers be exempt from collective-bargaining rights.
Sen. Evan Bayh, D-Ind., said he supports giving Bush the right to fire employees for national-security reasons, but wants to guarantee workers some rights.
"The only area of difference was whether they ought to have a right of appeal at some point down the road after they've been fired, to make sure it was for legitimate reasons, not political reasons," Bayh said on "Fox News Sunday." "I don't think you want to repeal these people's rights across the board."
Bush's chief of staff, Andrew Card, said the president wants the bill on his desk before the lame-duck session ends. He said on NBC that he expects Congress may be in session into December.
Bush's proposal would create the Cabinet-level agency by combining existing pieces of the federal bureaucracy into a 170,000-employee department.
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