Rep. Peter King (R-NY) says that Republicans in the House of Representatives have a "mandate" to prevent tax cuts for the rich and other Americans from expiring even though exit polls showed voters supported tax hikes.

"As far as Congress, Republicans feel strongly that tax rates should not be increased," King told CNN's Candy Crowley on Sunday. "Having said that, I think John Boehner -- Speaker Boehner has shown his willingness to work out an agreement here. That can be done by effecting deductions, loopholes -- which would include those in the upper brackets -- so that the president could get the revenue that he says that he's looking for, but it will be done in a way that tax rates are not increased."

He added: "So it can be said that while President Obama won -- and he did win -- the fact is in the Congress, the American people have returned a Republican House of Representatives. So we also have if you want to call it a mandate."

"Having said that, I think if there's any mandate, it's to try to reach compromise and try to reach common ground, and I think Speaker Boehner has put enough on the table that a real compromise can be reached."

In exit polls released on Tuesday, six in ten voters said they supported raising taxes. Almost half wanted to see tax hikes specifically on those making more than $250,000 a year.

"On this particular issue, it wasn't close," Obama campaign adviser David Axelrod told CBS News on Sunday.

"You need new revenues, and every objective person who has looked at this agrees on that, so the question is where is that revenue going to come from?" he pointed out. "The president believes it is more equitable to get that from the wealthiest Americans who have done very well and frankly don't need those tax cuts and who benefited disproportionately from the tax cuts in the last decade. Most Americans agree with that."

Watch this video from CNN's State of the Union, broadcast Nov. 11, 2012.