At stake were sweeping tax hikes and across-the-board spending cuts set to take effect at the turn of the year.
Economists warned the one-two punch could result in a big jump in unemployment and turmoil in financial markets and send the fragile economy back into recession.
Republican Senate minority leader Mitch McConnell spoke repeatedly to Vice-President Joe Biden to try to settling remaining differences.
The House and Senate met yesterday, a rarity for New Year's Eve, in hopes of having a tentative agreement to consider.
If an agreement is not approved by the start of today, more than $500 billion in 2013 tax increases will begin to take effect and $109 billion will be carved from government programmes
"There is still significant distance between the two sides, but negotiations continue," Democratic Senate Majority leader Harry Reid said earlier.
The fiscal cliff was caused by tax cuts, which were enacted in 2001 and 2003 when George W Bush was president, expiring yesterday.