(CNN) - With the "fiscal cliff" so close that its arrival is now measured in hours, President Barack Obama sent a clear message to the country Sunday: Republicans are responsible for the stalemate and must be pressured to do the right thing.
"They say that the biggest priority is making sure that we deal with the deficit in a serious way. But the way they're behaving is that their only priority is making sure that tax breaks for the wealthiest Americans are protected. That seems to be their only overriding, unifying theme," Obama told NBC's "Meet the Press" in an interview broadcast Sunday.
If nothing is done before Monday night at midnight, when the new year kicks in, the series of tax cuts that expires will hike up middle-class tax rates, damaging the economy and costing the average family about $2,000, he said, repeating the term "middle-class" numerous times throughout the interview.
The Senate is scheduled to convene Sunday at 1 p.m.; the House is scheduled to convene at 2 p.m.
If a broader deal cannot be reached, then the Senate should vote on legislation to make sure middle-class taxes are not raised and that 2 million people don't lose unemployment benefits, he said.
"If we can get that done, that takes a big bite out of the fiscal cliff," Obama said. "It avoids the worst outcomes."
Tough negotiations would then follow on the chief sticking point of the battle: whose taxes should go up. Democrats want them to go up for those making $250,000 or more. Discussions have involved the possibility of raising that figure to a $400,000 threshold, along with a push to keep estate taxes low; Democrats have said they might be open to one such scenario, but not both.
But many Republicans have opposed any increase in tax rates. House Speaker John Boehner, R-Ohio, suffered a political setback by offering a compromise -- a $1 million threshold for the higher rates to kick in -- that his GOP House colleagues refused to support.
Extending unemployment insurance was on the table in Senate negotiations under way Sunday, and the estate tax was under debate, according to a source familiar with the talks.
Negotiators worked late Saturday night, but not through the night, the source said.
Republicans argued Sunday that the resistance to Obama's plan is based on his refusal to adequately limit spending.
"The president is doing nothing about the addiction that his administration has to spending. He's the spender in chief," Sen. John Barrasso of Wyoming said on CNN's "State of the Union."
Republican Rep. Darrell Issa of California echoed those remarks. "Even if you put back all the revenue you would get from those higher taxes, you still have a deficit. That's what we're trying to change," he said.
Obama rejected such complaints, telling NBC that he has cut more than a trillion dollars in spending. "I offered over $1 trillion in additional spending cuts so that we would have $2 of spending cuts for every $1 of increased revenue," he said on NBC.
The president also emphasized that he had campaigned on "a balanced approach" which would increase taxes on the wealthy -- and that the majority of Americans have made clear they support such a plan.
The idea of maintaining tax cuts for 98% of Americans, while allowing tax cuts to expire for the wealthiest, was once part of "a pretty mainstream Republican agenda," he argued, adding that opposition "is an indication of how far certain factions inside the Republican Party have gone."
The interview, recorded Saturday, marked the president's first appearance on a political talk show in three years.
A spokesman for Senate Minority Leader Mitch McConnell, R-Kentucky, said Sunday, "While the president was taping those discordant remarks yesterday, Sen. McConnell was in the office working to bring Republicans and Democrats together on a solution."
Sen. Lindsey Graham, R-South Carolina, said the chances are "exceedingly good" that some type of deal will be reached by Monday night.
"I think, whatever we accomplish, political victory to the president, hats off to the president. He stood his ground. He's going to get tax rate increases, maybe not (on people making) $250,000, but upper-income Americans," Graham said on "Fox News Sunday."
"And the sad news for the country is that we have accomplished little in terms of not becoming Greece or getting out of debt."
At stake in the negotiations, according to numerous economists, is the fate of a still fragile U.S. economy that could be pushed back into a recession by the broad tax hikes and automatic $110 billion cuts to domestic and military spending spelled out by the fiscal cliff legislation.
Obama and Democrats have leverage, based on the president's re-election last month and Democrats' gains in the House and Senate in the new Congress. In addition, polls consistently show majority support for Obama's position on taxes, and Democrats insist the House would pass the president's plan, with Democrats joined by some Republicans,
if Boehner allowed a vote on it.
"It is time for everybody to be all in," Sen. Debbie Stabenow, D-Michigan, said Sunday on CNN's "State of the Union," calling for the wealthiest to pay higher tax rates. "This is common sense. This is about everybody participating to solve the problem."
Conservative activist Grover Norquist has vowed to back primary challenges against Republicans who violate his widely signed pledge not to raise taxes. Even if a deal is reached, Norquist has predicted yet more budget showdowns every time the government needs additional money to operate.
The saga has fueled disdain for politicians by many Americans. Such contempt is deserved, said Rep. Steven LaTourette, an Ohio Republican, who is retiring from Congress.
"I think America should be embarrassed by its leadership in D.C.," he told CNN on Friday. "The fact that we have been unable to do things, and instead worried about our next elections ... I think it's sinful."