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Both sides are confident the US House of Representatives will pass a bipartisan Senate Bill to raise the debt ceiling, a senior Democratic aide has said.
A vote in both chambers, probably starting with the House, is expected later today.
The aide added that the measure is expected to pass the House with mostly Democratic votes.
Republican and Democratic leaders in the US Senate have struck a deal to raise the debt ceiling and avert a potential default, Republican senator Kelly Ayotte has told the Associated Press.
The measure still has to pass a deeply divided, Republican-controlled House of Representatives that failed twice on Tuesday to produce its own plan.
Republicans in the US House of Representatives are not planning to vote on legislation to end the debt standoff on Tuesday and will continue talks on Wednesday, according to Republican representative Pete Sessions.
The credit rating agency Fitch has placed the USA's 'triple-A' rating on a negative watch because of the ongoing stand-off in Congress.
Explaining its move, Fitch says that although it believes the debt ceiling will be raised soon, the "political brinkmanship and reduced financing flexibility could increase the risk of a US default".
House Republicans will try to advance a new compromise bill that raise the debt ceiling until February 7 with a "hard cut-off," Representative Devin Nunes has said.
Nunes, a Republican from California, told reporters that the latest plan would include new changes to the 'Obamacare' health bill for Congress and high-ranking Obama administration officials.
US President Barack Obama will meet Nancy Pelosi, the Democratic leader in the House of Representatives, and other House Democratic leaders, the White House said in a statement.
The meeting, scheduled for 3:15pm local time (8:15pm UK time), comes as the White House rejected a proposal by House Republicans to end the stalemate as "partisan".
The White House has issued a stern response to the latest proposal on raising the debt ceiling from the House Republicans, accusing it of being partisan:
Republicans in the House of Representatives are working on their own plan to end the fiscal stand off in the US and avert a possible default, NBC News reports.
It comes as the Senate is putting the finishing touches to a bipartisan plan to raise the debt ceiling - the latest in a series that have foundered on Republican opposition in the House.
NBC News reports that House Republicans will vote on the plan - which would delay certain aspects of Obamacare - as early as today.
US Senate Majority Leader Harry Reid has said there has been "tremendous progress" towards the debt limit and a government funding deal.
Senate Republican Leader Mitch McConnell echoed this progress, but Reid made it clear they "are not there yet".
Latest ITV News reports
As Thursday's debt ceiling deadline looms, the most powerful nation in the world suddenly looks weak and dysfunctional.