Democratic Senate Majority Leader Harry Reid says he is "optimistic" there will be positive outcomes in efforts to reopen the government and raise the debt ceiling.
Reid spoke on the Senate floor at the close of a rare Sunday session.
Reid said he and Republican leader Mitch McConnell held productive talks but gave no specifics.
Earlier, Reid criticized Senate Republicans who rejected a Democratic plan to raise the government's borrowing limit through next year. House Republicans have proposed a short-term increase and want any extension to include spending cuts.
International Monetary Fund managing director Christine Lagarde told NBC-TV's Meet the Press Sunday that failing to increase the debt ceiling would mean "massive disruption the world over" and could increase the risk of another global recession.
The current debt ceiling expires Thursday. If Congress does not raise it, the United States could no longer borrow money to pay its creditors or meet other obligations.
Also, the partial government shutdown starts its third week Tuesday with no clear signs of progress between Congress and the White House.
Reid said last week the shutdown is causing pain and suffering across the country. President Barack Obama and Democrats are demanding Congress pass a so-called clean spending bill before negotiating on other issues, such as spending cuts and his health care program. Many Republican want negotiations before voting on a budget.
Christine Legarde, IMF Managing Director:
"You have to honor your signature, you have to give certainty to the rest of the world and you have to make sure that your own economy is consolidating that welcome economy that we have seen in the last few days, because it impacts the entire economy."