Warner, who was a member of the “Gang of Six,” which tried to broker a deficit deal last year, said lawmakers recognize the consequences of going over the “fiscal cliff," which will come at the end of the year when the Bush-era tax rates expire and automatic spending cuts take effect.

“There is an enormous recognition of the consequences to our economy if we go over the cliff," Warner said.

Democrats have said any deficit reduction plan must allow the Bush tax rates to expire for those making more than $250,000. Republicans argue that any tax increases would harm small businesses and more recently have said the entitlement reform must be included in a deficit reduction package if it’s to pass the GOP-controlled House.

Warner said that the divisiveness of the November election would make it difficult for both sides to come together.

"One of the challenges, particularly in the aftermath of the election is, even if you've got a great plan, it may be hard for the leaders on both sides to immediately agree," Warner said. "So, if we have to take the first few whacks to narrow the playing field so that the Speaker and the president … can get us faster and quicker to a 'yes,' that may be some value. But we'll have to see how this will continue the leadership discussion and play out."

On Friday, President Obama invited congressional leaders to the White House to being discussions of how to move forward with a deficit reduction package.

Warner said reaching a deal by the end of the year was crucial for U.S. job growth.

"And, it will do enormous amount of value in terms of restoring America's confidence, particularly as we go into the very important retail holiday season, that the folks they've hired are actually going to put country over partisan interests," Warner said on the radio show.