However, details on how policymakers will do so remain unclear.
Key sticking points that have kept the two parties at odds is that Democrats widely favor increasing taxes on wealthy Americans, while Republicans maintain that the answer to the bulging fiscal deficit is to slash federal spending.
With just weeks until the cutoff date, it appears each side is ready to make some concessions.
Tennessee's GOP Sen. Bob Corker acknowledged Sunday on Fox News that the nation's wealthiest should shell out more in taxes. But, he added, the increases should come from closing loopholes instead of boosting tax rates. Corker added that cuts to entitlement spending would also need to be considered for Republicans to approve any pact.
"I'm optimistic on a deal," the Senator said. He went on to say he thought a "basis for the deal" was in place.
Corker continued, "I think finally, Democrats are willing to accept-and I don't mean this pejoratively, but I think they know that Republicans really are willing to put revenues on the table if we can do it in a pro-growth way, and there is a way of doing that."
In addition, David Axelrod, a senior adviser to U.S. President Barack Obama's re-election campaign said Sunday on CBS's "Face the Nation" he believed the Republican comments regarding the fiscal cliff are "encouraging."