House Republican leaders delivered a $2.2 trillion “fiscal cliff” counteroffer to President Obama on Monday that included $800 billion in tax increases, but the White House and congressional Democrats said that still isn’t enough revenue to begin negotiating.

The GOP outline, which came in a letter from House Speaker John A. Boehner and his top lieutenants to Mr. Obama, called for $900 billion in cuts to projected entitlement spending and would also use a lower inflation measure to calculate future Social Security benefits.

Mr. Boehner told reporters he was trying to craft a middle-ground starting point after the White House last week proposed what he called a “la-la-land offer” that asked for $1.6 trillion in new taxes and up to $400 billion in potential spending cuts.

“That couldn’t pass the House, couldn’t pass the Senate and it was basically the president’s budget from last February,” the Ohio Republican said, referring to legislation that was defeated on unanimous votes in both chambers earlier this year.

The Republicans said they could raise taxes $800 billion by ending loopholes for the wealthy rather than raising their income tax rates, but the White House has insisted most of the new money must come from higher rates.

“The Republican letter released today does not meet the test of balance,” White House Communications Director Dan Pfeiffer said. “Their plan includes nothing new and provides no details on which deductions they would eliminate, which loopholes they will close or which Medicare savings they would achieve.”

He said Mr. Obama “is willing to compromise” but that won’t happen until Republicans “get serious about asking the wealthiest to pay slightly higher tax rates.”

Both sides are rushing ahead of a year-end deadline to avoid across-the-board tax increases and $110 billion in automatic spending cuts, which have been dubbed the fiscal cliff. Together, they would plunge the country into a short, sharp recession, but would leave it in better fiscal and economic shape over the long run, the Congressional Budget Office said.

Lawmakers, though, want to minimize the pain. All sides want to extend the lower tax rates for most Americans, leaving the chief dispute over what happens to the tax cuts for couples making $250,000 or more a year.

The GOP made a major concession Monday when Mr. Boehner and his top House Republican allies said they would be willing to accept $800 billion in new taxes from those high-income taxpayers.

Republican leaders had said they would be willing to consider revenue but had left it vague whether that money would come from real tax increases or from the economic benefits of expanded growth. On Monday, top congressional aides said it would be real revenue under the definitions of the Congressional Budget Office, which is the official scorekeeper for these matters.

The new stance surprised some key Republicans.

Rep. Jim Jordan of Ohio, head of the Republican Study Committee caucus, said he did not know that House leaders planned to roll out their framework for averting the fiscal cliff.

“My general reaction is the good news is that it is obviously better than the bullet points the president gave, which was ridiculous,” Mr. Jordan said. “The bad news is that it is a tax increase and I am not going to vote for a tax increase because it hurts economic growth.

“If you are going to lower rates and close loopholes and do genuine tax reform, that is one thing because that contributes to economic growth,” he said. “But if you are going to raise taxes through closing loopholes, deductions, that is not economic growth. That is just a different way to raise taxes.”

Grover Norquist, president of Americans for Tax Reform and the man who runs the influential no-new-taxes pledge, had urged the Republicans to hold firm in rejecting any tax increase. An ATR spokesman said the group didn’t have enough details Monday to evaluate the plan.

Much of the debate comes down to whether it’s possible to squeeze $800 billion in revenue out of the wealthy through loopholes alone. Mr. Boehner says it is possible, while Mr. Obama and his allies say it isn’t.

Democrats said until Mr. Boehner agrees to rate increases, nothing can be negotiated.

“Republicans are simply digging in their heels by refusing to ask the wealthiest Americans to pay their fair share and actually calling for lower tax rates,” House Minority Leader Nancy Pelosi said.

The Republican offer comes five days after Treasury Secretary Timothy F. Geithner met with congressional leaders and laid out broad targets that included $1.6 trillion in new tax increases, and hundreds of billions in new stimulus spending and extended benefits for the unemployed.

Mr. Boehner said the last time he talked personally with Mr. Obama was Wednesday, though the two sides hinted they could talk on the sidelines of the White House holiday ball Monday night.

The GOP plan doesn’t lay out specific tax increases or spending cuts but instead gives broad goals to achieve the $2.2 trillion in lower deficits over the next decade: $800 billion in revenue, $600 billion in lower projected health spending, $300 billion from other entitlements, $200 billion by lowering automatic increases in spending and benefits, and another $300 billion from annual discretionary spending.

The Republicans’ offer says nothing about Mr. Obama’s call for more stimulus spending or about his demand that Congress give up its power to control the federal debt ceiling, which Republicans hope to use to keep an upper limit on spending.

• Susan Crabtree contributed to this report.

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