Updated at 12:12 p.m.

House Speaker John Boehner’s (R-Ohio) comments last week regarding the so-called fiscal cliff were “encouraging,” President Obama’s senior campaign strategist David Axelrod said Sunday morning.

“His rhetoric has been encouraging and I think we've also had an intervening election,” Axelrod said on CBS’s “Face The Nation.”

Last week, Boehner opened the door to the possibility of using new revenue to rein in the nation’s debt. He said later in the week in an interview, though, that raising tax rates is “unacceptable.”

Axlerod said that Obama’s reelection demonstrated that the American public largely agrees with the president's stance on taxes.

“If you look at the exit polls I think it was somewhere around 60 percent of the American people agreed with the president's position on this issue of taxes. It is obvious that we can't resolve the challenge here simply by cutting the budget, we've cut by a trillion-one, there are more cuts to be made, but you need new revenues,” Axelrod said.

Sens. Patty Murray (D-Wash.) and Saxby Chambliss (R-Ga.) addressed the fiscal cliff and the nation's debt on ABC's "This Week With George Stephanopoulos," with the Democrat echoing Obama's call for the wealthiest Americans to pay more in taxes and the Republican arguing that revenue increases need to be pursued in the right way. 

"Clearly, we have the ability between now and the end of the year to not go off the cliff," Murray said. "But we can't accept an unfair deal that piles on the middle class and tell them they have to support it.  We have to make sure that the wealthiest Americans pay their fair share."

She added that "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.  And whatever we do will be a tax cut for whatever package we put together.  That may be the way to get past this."

"Speaker Boehner said it I think very well, I thought he showed great leadership by saying that revenues need to be on the table," Chambliss said. "Again, we need to do it in the right way. Bowles-Simpson said, look, eliminate all these tax credits and tax deductions. You can generate somewhere 1 to 1.2 trillion in additional revenue. You can actually lower tax rates by doing that. And I think at the end of the day, what's got to happen."