Senator Reid said there were still significant differences between the two sides US Congressional leaders have one more day to stop the threat of steep tax rises and spending cuts, known as the "fiscal cliff", after talks ended with no deal.Senators will continue to seek a compromise deal on Monday to send to the House of Representatives.
Failure to reach agreement by 1 January could push the US back into recession.
Earlier, President Obama increased pressure on Republicans to accept a deal, blaming them for the deadlock.
He said their "overriding theme" was protecting tax breaks for the rich.
Fallback plan Continue reading the main story Adam Blenford BBC News, WashingtonFew in the US capital could talk of anything but who would win Sunday's must-win showdown. For most, that meant an NFL game between the Washington Redskins and the Dallas Cowboys; on Capitol Hill the stakes were somewhat higher.
Cliches and aphorisms abounded in the Senate corridors as reports spread of a breakdown in deal-making. "The fat lady hasn't sung yet," one Republican declared, obscured by the pack of reporters following him down the hallway. "These things always happen at the end," said Chuck Schumer, a senior Democrat.
But it was the retiring senators, three days away from their final goodbyes, who spoke the most openly. Failure would "send a message worldwide that we don't have the capacity to work across political aisles on critical issues", said Olympia Snowe, Maine's outgoing Republican.
"The world has gotten used to this so they are no longer shocked," Ben Nelson, a retiring Nebraska Democrat said. "They see this as just more of the same and hope that one of these days maybe Congress will get its act together."
Talks ended on Sunday with no deal after a day that saw Republican and Democratic senators wrestle over detail and seek to shape a final bill.Sticking points included the fate of expiring Bush-era tax cuts, an estate tax and steep cuts in spending known as the sequester.
If no agreement is reached on Monday, senators are expected to be given the chance to vote on a fallback plan proposed by President Obama.
That would renew tax cuts on earnings under $250,000 (£154,000) and extend unemployment benefits, but does not address the steep spending cuts.
The current stand-off has its roots in a failed 2011 attempt to tackle the government debt limit and budget deficit. Republicans and Democrats agreed then to postpone difficult decisions on spending until the end of 2012, and imposed a threat of compulsory cuts if no deal was reached by 31 December.
Analysts say that even if a deal is reached on the fiscal cliff, it will do little to reduce the original problem of the deficit and the government debt limit, raising the prospect of further political in-fighting early in the new year.
Parties dividedSenate Democratic leader Harry Reid and his Republican counterpart Mitch McConnell were locked in negotiations over the weekend.
The two senators appeared to admit not long before the 15:00 deadline (20:00 GMT) that negotiations were at a standstill, with their two parties still divided over core ideological issues about tax and government funding.
Senator Reid said the Democrats were as yet unable to make a counter-offer to an apparent Republican proposal to slow cost-of-living increases for social security recipients, known as "chained CPI".
Continue reading the main story On 1 January 2013, tax increases and huge spending cuts are due to come into force - the so-called fiscal cliff Deadline was put in place in 2011 to force president and Congress to agree ways to save money over the next 10 yearsDate coincides with expiry of Bush-era tax cuts, which would affect all income groups and many businessesFear is that raising taxes while massively cutting spending will have a huge impact on households and businessesExperts believe it could push the US into recession, and have a global impact on growthMeanwhile Senator McConnell said he had asked Vice-President Joe Biden for help in breaking the deadlock."I'm concerned with the lack of urgency here. There's far too much at stake," he said. "There is no single issue that remains an impossible sticking point - the sticking point appears to be a willingness, an interest or courage to close the deal."
In his interview with NBC's Meet the Press, broadcast on Sunday, Mr Obama said the priority was to ensure taxes do not rise for middle-class families, saying that would "hurt our economy badly".
"That's something we all agree on. If we can get that done, that takes a big bite out of the 'fiscal cliff'," he said.
There is also debate over where to set the threshold for tax rises. Democrats say the Bush-era tax cuts should be extended for all Americans except the richest - those with annual earnings of more than $250,000 (£155,000).
Republicans - some of whom have pledged never to vote for increased taxes - say the deficit is a consequence of excessive government spending.
They want the tax threshold set higher, at around $400,000, and for revenue to be raised by economic growth and cuts in social security and other services states are legally bound to provide.
