The warning came as some Republicans urged House Speaker John Boehner to stop fighting tax increases for the wealthiest 2 percent of taxpayers and President Obama traveled to the apartment of a middle class family in Virginia fearing a possible $2,200 increase in their tax bill if no agreement is reached.
The nation faces a Jan. 1 deadline for the expiration of the Bush-era tax cuts and draconian budget cuts that could send the economy back into recession.
Boehner said Monday negotiations are at a standstill and Treasury Secretary Tim Geithner said Wednesday the White House is "absolutely" prepared to go over the "fiscal cliff."
"If there is no agreement, then the fiscal cliff has to be dealt with," Pelosi said Thursday. "Let's hope that we can have an agreement."
Late Thursday, The Wall Street Journal reported talks between Boehner's office and the White House had resumed.
"Lines of communication are open," Boehner Michael Steel said.
Pelosi called the Republican plan calling for $800 billion in revenue and $900 billion in spending cuts "an assault on the middle class, on our seniors and on our future," CBS reported.
"It was not in furtherance of finding common ground," she said.
Obama has called for $1.6 trillion in new revenue -- $950 billion coming from incomes of more than $250,000 -- and $2.4 trillion in spending cuts.
Obama visited the ground floor apartment of Tiffany Santana of Falls Church, Va., a high school English teacher, who responded to the president's email encouraging people to share their stories about how paying $2,200 more in taxes next year would affect their families. She and her husband Richard live with their son Noah, 6, and her parents.
"They're keeping it together, they're working hard, they're meeting their responsibilities. For them to be burdened unnecessarily because Democrats and Republicans aren't coming together to solve those problems gives you a sense of the costs on personal terms," Obama said.
Obama reiterated he will not sign any legislation that does not raise taxes for the wealthiest 2 percent of U.S. taxpayers.
GOP lawmakers said Wednesday they were willing to discuss raising rates on taxable income above $250,000 because they saw that concession as clearing the way for a broad deal that would also rein in the cost of Social Security and Medicare, The Washington Post reported Thursday.
"I and some others are advocating giving the president what he wants," Rep. Steven LaTourette, R-Ohio, told the newspaper.
He stressed this concession must be part of a package that slows federal borrowing and reduces the debt $4 trillion to $5 trillion.
"Quite frankly, some people in this 2 percent who call me, they're more worried about the fiscal cliff than about the rates going up a couple points. That has bigger risk for them," said LaTourette, who is retiring in January.
Rep. Thomas Rooney, R-Fla., told the Post, "If there are truly real entitlement reforms that are going to preserve Social Security and Medicare for generations to come, it's going to be very difficult for me to oppose" higher tax rates for the rich.
Sen. Tom Coburn, R-Okla., a fiscal and social conservative, told MSNBC: "Personally, I know we have to raise revenue. I don't really care which way we do it. Actually, I would rather see the rates go up than do it the other way, because it gives us a greater chance to reform the tax code and broaden the base in the future."
Boehner told reporters Wednesday: "I believe it is appropriate to put revenues on the table. Now, the revenues that we are putting on the table are going to come from -- guess who? -- the rich."
Republicans are increasingly worried they could be blamed if Washington doesn't resolve the impasse.
The U.S. government has $16.308 trillion in debt, putting it just beneath the $16.4 trillion limit set by Congress. The government is expected to run out of emergency measures to avoid hitting the debt ceiling by February or March, the Congressional Budget Office has said.
Obama warned Republicans Wednesday not to pursue a course that would set up a fresh battle over the debt limit, like the U.S. debt-ceiling crisis of July and August 2011, which Obama called a "catastrophe."
"I want to send a very clear message to people here: We are not going to play that game next year," Obama told the Business Roundtable trade group, referring to Republicans using the debt limit to negotiate further spending cuts.
"That is a bad strategy for America, it's a bad strategy for your businesses, and it is not a game that I will play," Obama told the big-business executives.