The next line of Republican attack: Spending cuts. Republicans are promising $100 billion of cuts over the next eight months. But so far the only specific they've offered is a $35 million cut in Congress's own budget, which means a slight reduction in things like staff salaries and office supplies.
The specifically mentioned cuts add up to less than four one-hundreths of 1 percent of the $100 billion cut they've promised.
But behind the scenes, much of the talk is about an issue both sides would much rather avoid: the national debt, which this week shot to more than $14 trillion.
In the coming months, the government hits the limit of the amount it can legally borrow -- $14.3 trilliion. If the debt ceiling is not raised, the United States effectively starts bouncing its checks and faces a government shutdown, or worse.
While a top Obama economic adviser said Sunday the repercussions of the government defaulting would be worldwide and "catastrophic," some tea party Republicans are saying they'll refuse to allow the government to borrow more money.
"I could not be more serious when I say I'm not going to vote to increase the national debt limit," Sen.-elect Mike Lee, R-Utah, told ABC in November.
Rep. Michael Burgess, R-Texas, told ABC's Top Line Tuesday that "I have voted for it [to raise the debt limit] in the past and it was one of the worst things I ever did in my life. I will not go there willingly again."
Burgess, like many of his Republican colleagues, said he wants to see significant cuts in spending before he makes any vote on raising the debt ceiling.
"I think we should use this as an opportunity to really begin to get our arms around the amount of federal spending," Burgess said. "I understand that this is our opportunity to really get some meaningful change in the way this country spends its tax dollars. And the president has to be willing to work with us."
The president, for his part, has extended the olive branch to Republicans. He said in a YouTube message Sunday that he welcomes ideas from both sides of the aisle, but could find it very difficult to swallow some of the spending cuts being demanded by Republicans.
"We have got a full agenda of cutting and growing," Cantor said. "And we are going to be about demonstrating our commitment to cutting spending every single week that we are here."