Talks are ongoing, a senior GOP aide told ABC News, while cautioning that it is unlikely that details of a deal will emerge before McConnell and Reid brief their caucuses Sunday afternoon.
If the Senate talks fail, Obama has instructed Reid to bring the Democratic proposal to the floor as a backup. That plan would raise taxes on couples making more than $250,000.
In his weekly address, Obama again pressed for swift action and expressed cautious optimism.
"Sens. Reid and McConnell are discussing a potential agreement where we can get a bipartisan bill out of the Senate and over to the House in a timely fashion so that we meet the Dec. 31 deadline," Obama said. "But given how things have been working in this town we always have to wait and see to see whether it actually happens."
In the weekly GOP response, Sen. Roy Blunt, R-Mo., said the cliff could be avoided while calling for the Senate to pass a House-approved bill that would prevent any taxes from going up--a plan rejected by Democrats and campaigned against by Obama during the presidential race.
"Fortunately, going over the fiscal cliff is avoidable. There's not much time, but there is still time to act," Blunt said. "Instead of working across the aisle and considering the House-passed plan to protect taxpayers, Senate Democrats have spent months drawing partisan lines in the sand."
With those lines firmly drawn, Congress appears closer than ever to going over the cliff.