With the election over, the hot new thing that all the cool kids on the Sunday political chat shows were talking about today was the looming fiscal cliff and what Congress should do about it -- and you’ll be surprised by one recommendation.

The tax increases and government spending cuts set to go into effect early next year are so massive that they could plunge the economy back into recession, unless Congress figures out a less painful way to reduce the deficit. The argument has so far broken down along the predictable partisan lines that we’ve seen in countless congressional battles over the past few years. Democrats want a balance of spending cuts and tax increases, while Republicans insist on zero tax increases, and maybe not even a dime in new revenue increases of any kind.

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But just as the election has chastened Republicans on immigration, it may be doing the same thing on taxes. Bill Kristol, the editor of the Weekly Standard and one of the most prominent establishment conservative voices in Washington, threw the door wide open to tax hikes as part of fiscal cliff negotiations today. "It won't kill the country if we raise taxes a little bit on millionaires ... It really won't, I don't think. I don't really understand why Republicans don't take Obama's offer," he said on "Fox News Sunday."

He continued: “Really? The Republican Party is going to fall on its sword to defend a bunch of millionaires, half of whom voted Democratic and half of whom live in Hollywood and are hostile?" It's a remarkable statement, coming from Kristol.

Kristol has often clashed with Tea Party conservatives, but certainly holds the almost religious devotion to tax cuts that is the bedrock principle of the modern Republican Party. It’s the one thing that unites Ronald Reagan’s “three-legged stool” of the conservative coalition -- free marketeers, social conservatives and national security hawks. Even more dramatic than Sean Hannity’s immigration shift, Bill Kristol’s shift on taxes suggests the party (or at least some leaders in it) have been shaken to their core by the election. While immigration is one of many important second-tier issues , taxes are the issue to the GOP, so compromising here is a much bigger deal. “At current velocity some Republicans will be calling for carbon tax and single payer health care by end of the year,” the New Yorker’s Ryan Lizza quipped on Twitter in regards to Kristol’s remark.

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If Kristol’s remarks represent a nascent shift in the party (it's too early to tell at the moment), then it certainly bodes well for fiscal cliff negotiations and the future of the country, which will need tax cuts to deal with the deficit. One thing’s for sure, Kristol will likely be getting an angry phone call later today from Grover Norquist, the enforcer of the party’s anti-tax orthodoxy.

On the Democratic side of the equation, Washington Sen. Patty Murray took a hard line on fiscal cliff negotiations and suggested that Democrats should be willing to go over the cliff if need be, a welcome sign for progressives who are worried that President Obama will cave too easily. “We can't accept an unfair deal that piles on the middle class and tell them they have to support it,” she said on "This Week" on ABC. “So if the Republicans will not agree with [revenue increases], 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.”

By the way, you can expect to see a lot more of Murray during the lame duck session of Congress and next year. Murray, the chairwoman of the Democratic Senatorial Campaign Committee, just led one of the most impressive electoral efforts in recent memory, picking up two seats for Democrats in a year when they should have lost many more than that. These victories will likely elevate her within the party.

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Meanwhile, elsewhere on the chat shows, Republicans debated their future. CNN’s "State of the Union" assembled a panel seeking to represent various factions of the conservative movement. There was Gary Bauer, a staunch social conservative; Jon Huntsman, a moderate with crossover appeal; Carlos Gutierrez, George W. Bush’s commerce secretary, who has worked to reach out to Hispanics; and Rep. Cathy McMorris Rodgers, who led outreach to women for Mitt Romney’s campaign.

The panel was representative of the party today in that it was fairly neatly divided into two camps. The moderates said the party needs to moderate some, especially its rhetoric, with Gutierrez saying Latinos were "scared of the Republican Party” this year with all of its language of self-deportation and illegals. Bauer, naturally, opposed this. "We don't need two liberal parties,” he said, before telling Gutierrez that Hispanics don’t care about immigration. (“Pretty ridiculous to see Gary Bauer lecture Sec. Carlos Gutierrez about what is important to Hispanics,” tweeted Ana Navarro, who advised John McCain’s presidential campaign on Hispanic outreach.) McMorris Rodgers agreed: “I don't think it's about the Republican Party needing to become more moderate.”

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On "Meet the Press," Sen. Charles Schumer, a Democrat from New York, announced that he was restarting talks on comprehensive immigration reform with Lindsey Graham, a Republican from South Carolina who has called for his party to moderate on immigration. "The Republican Party has learned that being anti-immigrant doesn't work for them politically. And they know it,” Schumer said, explaining why he thinks his bill could succeed this year, even though similar efforts have failed in the past.

Beyond the Beltway, CNN’s Candy Crowley checked in with Jerry Brown, the Democratic governor of California, where Dems won huge victories Tuesday. Voters approved a referendum to raise taxes on the wealthy and also installed a Democratic supermajority in both houses, which is critical in a state that requires supermajorities to raise taxes. Brown noted that the national anti-tax movement started in California over 30 years ago and said the state is now starting a wave of more pragmatic approach to taxes.

As governor of a state with one of the most oldest medical marijuana laws in the country, he said the federal government needs to back off of California, along with states like Washington and Colorado, which just passed marijuana legalization laws. It should be up to them on how to regulate the drug, he said. “Be careful, you’re sounding like a Republican,” Crowley joked of Brown’s states' rights talk. Still, Brown said he opposed full legalization in his state.

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Finally, there was lots of talk, of course, about the resignation of David Petraeus as the head of the CIA. Senate Intelligence Committee Chairwoman Dianne Feinstein, a Democrat from California, told "Fox News Sunday" that she plans to investigate the FBI for failing to give her and other committee members advance notice about their discovery of Petraeus’ affair. She said the FBI is required to keep her committee abreast of developments like this, but failed. Rep. Peter King, the Republican chairman of the Homeland Security Committee, was suspicious, saying the FBI had known about the affair for months, but failed to inform the president. “The FBI should have had an obligation to tell the president ... It just doesn’t add up,” he told CNN’s "State of the Union." And Sen. Saxby Chambliss, the Republican ranking member of the Intelligence Committee, said he still expects Petraeus to testify at some point on what went wrong in the attacks on U.S. diplomats in Libya.