WASHINGTON (CNN) -- House Speaker John Boehner on Tuesday proposed letting tax rates go up on income above $1 million as a short-term step to avoid some of the fiscal cliff while continuing to negotiate a broader deal with President Barack Obama.
The White House and Democratic leaders immediately rejected Boehner's move, saying the focus of the incremental negotiations should be a comprehensive deficit-reduction agreement.
The back-and-forth in the halls of Congress came two weeks from the end of the year, when automatic tax hikes and spending cuts of the fiscal cliff will take effect.
At a news conference after meeting with House members Tuesday, Boehner called his new proposal a "Plan B" to avoid tax rates rising on everyone next year as part of the fiscal cliff.
It was the latest in a series of concessions by both sides since last week's school shooting in Connecticut that killed 20 youngsters and six adults.
"It will not protect middle-class families because it cannot pass both Houses of Congress," Senate Majority Leader Harry Reid of Nevada said in a statement.
Meanwhile, a White House statement called Boehner's Plan B approach insufficient, saying "It can't pass the Senate."
Boehner already had conceded on higher tax rates for wealthy Americans as part of the broader talks on an agreement to reduce the nation's chronic federal deficits and debt. His plan B proposal Tuesday further demonstrated the lack of leverage Republicans have on the issue.
Obama has made clear that allowing tax rates to go up on top income brackets was a non-negotiable demand in order to ensure that the wealthy contribute more to deficit reduction.
Under Obama's plan, which polls consistently show has strong public support, tax rates from the Bush era would be extended for families who earn less than $250,000. The higher rates of the 1990s would be assessed on incomes above that threshold.
As part of the broader talks, Obama on Monday raised the threshold for the higher tax rates to $400,000. The Boehner proposal would set the threshold at $1 million.
According to sources familiar with the negotiations, Boehner's plan B approach was expected, and the broader agreement still under negotiation remains the desired outcome.
Boehner told reporters that it was important to have a "back-up plan" to hold down most tax rates while continuing to negotiate a broader agreement. A Republican source told CNN that Boehner's plan B would include GOP priorities to make permanent the current estate tax and alternative minimum tax.
In his statement, Reid said Boehner should focus on a broader deficit-reduction deal, adding that the backup plan appeared to be due to pressure from tea party conservatives opposing a wider deal.
"It would be a shame if Republicans abandoned productive negotiations due to pressure from the tea party, as they have time and again," Reid said.
Obama previously said that once Republicans agreed to higher tax rates on wealthy Americans, he would be willing to compromise on spending cuts and entitlement reforms sought by Boehner as part of what the president calls a balanced approach.
On Monday, Obama responded to the latest GOP counteroffer with concessions on tax increases and spending cuts, according to a source familiar with the discussions.
Obama's latest offer brought the two sides billions of dollars closer, but it also generated protests from some in the Democratic base because it included some benefit cuts in entitlement programs, such as Social Security, Medicare and Medicaid.
Justin Ruben, executive director of MoveOn, the liberal movement that backed Obama's presidential campaigns, said the group's members would consider any benefit cuts "a betrayal that sells out working and middle-class families."
In particular, he cited concessions that Obama made in his Monday counteroffer, including a new formula for the consumer price index (CPI) applied to benefits.
"If such a deal were proposed by the president and speaker, MoveOn members would expect every Senate and House Democrat to do everything in their power to block it," Ruben said.
Over the weekend, Boehner offered for the first time to accept tax-rate increases on household income of $1 million and above, sources said. The speaker also offered to allow the president to raise the debt ceiling in 2013 without a messy political fight, another key Obama demand.
In response, Obama on Monday offered $200 million in new cuts to discretionary federal government spending, divided evenly between defense and nondefense programs.
The president also included for the first time the chained CPI sought by Republicans, and dropped an extension of a payroll tax cut from the past two years.
According to the source who provided CNN with details of Obama's counteroffer, it includes $1.2 trillion in revenue increases and $1.22 trillion in spending reductions.
However, Boehner disputed those figures Tuesday.
"The White House offer yesterday was essentially $1.3 trillion in new revenues for only $850 billion in net spending reductions," he said. "That's not balanced in my opinion."
Obama and Boehner met face-to-face at the White House on Monday for 45 minutes, their third such meeting in eight days in a sign of an acceleration in the fiscal cliff negotiations.
Boehner said he "made it clear to the president that I would put a trillion dollars worth of revenue on the table if he were willing to put a trillion dollars of spending reductions on the table."
Hours before news of the president's latest offer emerged Monday, White House spokesman Jay Carney made it clear that more work needed to be done.
"The president's proposal is the only proposal that we have seen that achieves the balance that is so necessary" between revenue and cost-cutting, said Carney, who refused to discuss specifics.
Congress had been scheduled to end its work last week, but legislators returned to Washington on Monday and leaders warned members to be prepared to stay until Christmas and return after the holiday until year-end.
Last week, U.S. Rep. Chris Van Hollen, D-Maryland, said a deal would have to be reached by Christmas to allow time for the legislative process to approve the required measure or measures by the end of the year.
Obama's latest proposal included $130 billion in spending savings due to changes in the CPI, which is applied to many entitlement benefits to protect participants against rising prices.
The chained CPI includes assumptions on consumer habits with regard to rising prices, such as seeking cheaper alternatives, and would result in smaller benefit increases in future years. Labor unions and advocacy groups for the elderly oppose it.
Republican aides estimate that the CPI would increase tax revenues by an additional $95 billion over Obama's estimated $1.2 trillion, putting the total revenue figure of the president's latest proposal closer to $1.3 trillion.
The GOP aides also do not count Obama's estimated $290 billion in savings on national debt interest accumulation because they do not consider these savings real cuts. Therefore, the Republican aides said, Obama's plan fails to offer a 1-1 ratio of spending cuts and revenue that Boehner would consider balanced.
Conservatives trying to shrink the federal government generally oppose increasing tax revenue. They are particularly opposed to higher tax rates because history shows that once rates go up, it is difficult to later reduce government revenue by lowering them again.
Obama and Democrats argue that increased revenue, including higher tax rates on the wealthy, must be part of broader deficit reduction to prevent the middle class from getting hit too hard.
CNN's Deirdre Walsh, Brianna Keilar, Gregory Wallace and Ted Barrett contributed to this report.