WASHINGTON » In their "fiscal cliff" standoff, President Barack Obama wants to raise taxes by about $20 billion a year more than House Speaker John Boehner. The president wants the government to spend about that much more yearly than Boehner does, too.

That’s real money by most measures. Yet such numbers are barely noticeable compared to the $2.6 trillion the government is projected to collect next year, and to the $3.6 trillion it’s expected to spend.

As the "cliff" approaches — economy-shaking tax increases and spending cuts that start hitting in early January unless lawmakers act first — each side says the other isn’t being serious enough about trimming federal deficits. But their inability so far to strike a compromise underscores that their problem is more than arithmetic — it’s also about the difficult politics that Democrat Obama and Republican Boehner face when it comes to lining up votes.

Chastened by Obama’s re-election, Boehner has violated a quarter-century of Republican dogma by offering to raise taxes, including boosting income tax rates on earnings exceeding $1 million annually. Eager for a budget deal that would let him move on to other issues, Obama in turn would cut the growth of Social Security benefits, usually off-limits to Democrats. He also would impose tax increases on a broader swath of people than millionaires — those with incomes over $400,000. But that figure, too, is a retreat from what he campaigned on: the $200,000 income ceiling on individuals and $250,000 on couples.

That means both men have angered lawmakers and staunch supporters of their respective parties, just when the need to retain that support is crucial.

"When you walk into a room and represent a group and you have to give ground to get a deal, you have to stay in that room as long as you can and you have to walk out with blood on your brow," said Joseph Minarik, research director for the Committee for Economic Development and a veteran of grueling budget talks as a former Clinton White House and House Democratic aide. "Otherwise, the people outside the room don’t believe you’ve fought hard for them."

With no quick resolution in sight, Boehner worked today to push a backup bill through the House that would raise taxes on people earning at least $1 million but not on those earning less. A separate bill would replace across-the-board cuts in defense and domestic programs with cuts in Obama’s health care overhaul and other specified programs.

Economists say the tens of billions of dollars separating the president and speaker are relatively minuscule, especially when compared to the size of the U.S. economy, which exceeds $15 trillion a year.

"It’s not vanishingly small, but it is minor," said Alan D. Viard, a tax scholar at the conservative American Enterprise Institute. "It certainly would be a disappointment if that minor of a gap would end up blocking an agreement."

Even though Obama’s and Boehner’s dollar differences are small, one hindrance to a deal could be the symbolic political consequence of retreating on their numbers, even just by a little.

For Boehner to add, say, another $100 billion to the tax increase over 10 years could well mean that people with incomes well below $1 million a year would get a tax increase, something he wants to limit.

On the other hand, adding $100 billion more in spending cuts could mean a deeper hit than Obama wants to Medicare. The president prefers to limit Medicare cuts to the reimbursements that doctors and other health care providers receive, but ever deeper cuts could mean more doctors would be likely to stop treating Medicare patients — an outcome Democrats don’t want.

None of this means there aren’t real budget differences between Democrats and Republicans.

Obama says he’s proposed raising taxes by $1.2 trillion over the coming decade by boosting the current top 35 percent rate to 39.6 percent for income over $400,000, plus other increases on the highest earning Americans. He’s also offered about $1.2 trillion in spending cuts over 10 years, including $400 billion from Medicare and Medicaid, the health care programs for the elderly and poor whose defense Democrats consider precious priorities.

Boehner has offered about $1 trillion in tax increases and about the same amount in spending savings. An earlier Boehner offer included $600 billion in Medicare and Medicaid savings — well more than Obama — but it’s unclear whether the speaker is still seeking that figure.

Because of a dispute over how some savings are classified, Boehner says Obama’s offer is really $1.3 trillion in higher taxes and only about $850 billion in spending cuts.

The House speaker says Obama’s offer is not balanced because its new taxes and spending cuts are unequal. And he complains it does too little to control fast-growing benefit programs like Medicare, a chief driver of the federal government’s mushrooming deficits.

"The real issue here, as we all know, is spending," Boehner said today. "You go through all these discussions, I don’t think the White House has gotten serious about the big spending problem the country faces."

The two men’s differences work out to $200 billion over 10 years in taxes, and about the same in spending, depending on whose numbers are used. Either way, their gap is less than 1 percent of the money the government will spend and tax anyway.

"They’re a couple hundred billion apart. This is absolutely senseless," said Senate Majority Leader Harry Reid, D-Nev., insisting Boehner should compromise. "These are gyrations I’ve never seen before."

There are other differences, too.

Obama wants several billion dollars in infrastructure spending to goose the economy and to extend expiring unemployment benefits. He also wants the government’s authority to borrow money extended for two more years — until after the 2014 congressional elections — with Congress having little more than symbolic opportunities to block it, a year longer than Boehner has offered.

Even so, the numbers being proposed by Obama and Boehner are so close, and the political risks both men have taken on taxes and Social Security benefits are so stark, that many consider it almost unthinkable that they would not eventually complete a deal.

"Having come out of their trenches, they either have to shake hands or get shot, maybe by their own troops," said Robert Bixby, executive director of the nonpartisan Concord Coalition, an anti-deficit group.

Associated Press writer Andrew Taylor contributed to this report.