(ABC News: Ma'ayan Rosenzweig)

With the "fiscal cliff" looming, there was plenty of talk today by members of both political parties of reaching a deal to avoid spending cuts and tax hikes that some economists say could plunge the country back into recession.

"We need to put politics aside. The election is over. President Obama has won," Republican Sen. Saxby Chambliss of Georgia said on ABC's "This Week."

But while there are signs of a way to make a deal, it's not clear that everyone is on board, even though Speaker of the House John Boehner says he will consider increasing revenues.

"The tone was good. I think the jury is still out on exactly what the substance of what he said is," Democrat Rep. Chris Van Hollen of Maryland said.

The so-called "cliff" comes on Jan. 1, when several tax cuts expire, and severe cuts to government spending are triggered. It's also been called "taxmageddon," because an average American family will see their tax bill increase $3,700 next year.

The sticking point to solve the stand-off is what the president calls a "balanced approach" of spending cuts and increased revenues. The president campaigned on, and won on, the pledge to allow the tax rates for the rich to rise, while keeping middle class tax rates where they are currently.

A leading Republican said "no" on Sunday.

"No Republican will vote for higher tax rates. We will generate revenue from eliminating deductions and loopholes," Sen. Lindsey Graham of South Carolina said on CBS' "Face the Nation."

That's the position Boehner is promoting as well.

While Obama has said he is open to "new ideas," a leading Democrat suggested closing loopholes is not enough. Sen. Patty Murray of Washington was asked on ABC's "This Week" if Democrats will allow the country to go over the cliff.

"To solve this problem, the wealthiest Americans have to pay their fair share, too," she said. "So if the Republicans will not agree with that, we will reach a point at the end of this year where all the tax cuts expire and we'll start over next year."

The two sides have a few more days to make their cases before Congressional leaders are called to the White House on Friday. That's when negotiations start in earnest and we learn if the election made a difference in relations between the two parties.