Hopes have risen for a congressional agreement thaqt could reopen the U.S. government and avoid a debt default.
As the partial federal government shutdown begins its third week, House and Senate members of both parties are to meet to discuss details of a potential deal.
The accord would increase the federal government's debt limit into early 2014, and would include a short-term measure to reopen the government and allow negotiations to begin on a budget for fiscal 2014, which began on October 1.
After talks Monday, Democratic Senate Majority Leader Harry Reid and Republican Senate Leader Mitch McConnell both expressed optimism. Reid predicted Tuesday could be a "bright day," and McConnell said he shares Reid's view.
Any deal would have to be approved by the full House and Senate before being signed by President Barack Obama.
If the debt ceiling is not raised by Thursday, the United States may not be able to pay all its bills. It is unclear whether Congress can meet that deadline even if Democratic and Republican party leaders reach an agreement in the Senate. Conservative hardliners such as Texas Republican Ted Cruz might force a delay in a final vote.
The House also would need to back the plan. Speaker John Boehner and other top Republicans are under strong pressure from conservative congressmen who oppose concessions. Many of them say they will refuse to back any deal that fails to alter the Affordable Care Act, the reform of the U.S. health care system that is now beginning to take effect.