But despite the anti-tax rigidity voiced by some Republicans, others kept their options open. On "Fox News Sunday", Sen. John McCain, R-Ariz., refused to rule out the possibility that a deal to avoid the sequester could include more revenue.

"We've got to avoid it, we've got to stop it," McCain said of the sequester. "Would I look at some revenue closers? Maybe so."

But that doesn't mean he would be happy about it. "We've already just raised taxes. Why do we have to raise taxes again?" he asked.

McCain also blasted what he saw as presidential disengagement on the issue. "What I would like to see is the president call the leaders over to the White House and say, 'Look, we've got to solve this problem," he said. "All he does is go out and make speeches."

On Tuesday, at least, the president will have no choice but to "go out and make speeches." And after Tuesday, more speeches: the president will hit the road, campaign-style, traveling to Asheville, N.C., Atlanta and Chicago to sell the economic proposals he will lay out Tuesday night.

Beyond his economic message, Mr. Obama is also expected to use the State of the Union to lobby for his three biggest second-term agenda items: immigration reform, climate change, and gun control.

Gun control, in particular, will be one of the most closely watched themes of the president's address. More than 20 House Democrats have announced that they will bring people affected by gun violence as guests to the address. And on Saturday, CBS News learned that former Rep. Gabrielle Giffords and her husband Mark Kelly will attend the speech as guests of Sen. John McCain and Rep. Ron Barber, D-Ariz. Giffords has emerged as one of the faces of gun violence in America after being shot in the head and nearly killed during a mass shooting in Arizona two years ago.

The official response to the State of the Union will be delivered by rising conservative star Sen. Marco Rubio, R-Fla., who is expected to stress limited government and free enterprise as the keys to economic recovery.