US Senate leaders have said they are nearing a deal to reopen the government and raise the US debt limit.

Senate Democratic leader Harry Reid and Senate Republican leader Mitch McConnell, who began talks on Saturday, appeared together on the Senate floor to voice their optimism that such a deal could be finalised within days.

If the full Democratic-led Senate passes it, the proposal would then go to the Republican-led House.

Democratic and Republican senators are working on a fiscal deal that would extend US borrowing authority at least through mid-February and provide government funding until mid-January to end a two-week government shut down, according to a source familiar with the negotiations.

The tentative framework, which is not finalised and could change, would also set up a new round of deficit-reduction negotiations that would try to strike a bargain by year's end.

The source, who asked not to be identified, said negotiators were still bargaining over whether the 15 February date for the debt limit extension would be a firm deadline or whether the Treasury Department would be allowed to use "extraordinary measures" to extend borrowing beyond that date, as it has done in the recent past.