WASHINGTON — House Speaker John Boehner said Tuesday that he is readying a backup bill aimed at averting the “fiscal cliff” because President Barack Obama has yet to offer a balanced package of revenues and spending savings that would cut burgeoning federal deficits.

Boehner’s measure would cancel tax increases due to take effect Jan. 1 on everyone earning $1 million or less, while allowing tax increases on those earning more than that amount.

“I continue to have hope that we can reach a broader agreement with the White House” that would cancel a broad wave of tax increases and spending cuts now poised to begin in early January, Boehner, R-Ohio, told reporters.

But he said when it comes to offering a package that balances tax increases with spending cuts, “The president is not there yet.”

Boehner said GOP efforts to cull savings from Medicare by increasing the eligibility age from 65 to 67 could wait until next year. That source of savings had been an important demand from Republicans earlier in Boehner’s negotiations with the White House.

Boehner aides said the call for a separate tax bill, which the speaker presented to his caucus Tuesday morning, does not mean the Republican is cutting off negotiations with Obama on averting the full slate of tax hikes and spending cuts due to take effect next year. Obama and Boehner have each made significant concessions in recent days, signaling a new stage in the negotiations.

Boehner’s latest move is an attempt to give Republicans political cover if Washington fails to reach a deal before the end of the year and taxes increase on all income earners. The White House had no immediate response to Boehner’s ‘Plan B’ proposal, but has previously rejected his attempts to extend tax cuts for families making up to $1 million.

However, the president has dropped his long-held insistence that taxes rise on individuals earning more than $200,000 and families making more than $250,000. He is now offering a new threshold of $400,000 and lowering his 10-year tax revenue goals from the $1.6 trillion he had argued for a few weeks ago.

Obama and Boehner met privately at the White House on Monday, and then spoke again on the phone later that night. Boehner huddled with House GOP members on Capitol Hill Tuesday morning to discuss the status of the talks and review Obama’s latest offer.

“We have to stop whatever tax rate increases we can,” Boehner said in the meeting, according to prepared remarks released by an aide. “In the absence of an alternative, as of this morning, a “modified Plan B” is the plan.”

Unless Congress acts, tax rates will increase on all income earners on Jan. 1. Boehner first opposed raising rates on any income earners, including the wealthiest Americans, but agreed on Friday to accept an increase in tax rates for taxpayers who earn more than $1 million. Boehner’s plan would raise about $1 trillion in taxes over 10 years.

In return, Obama also abandoned his demand for permanent borrowing authority. Instead, he is now asking for a new debt limit that would last two years, putting its renewal beyond the politics of a 2014 midterm election.

And in a move sure to create heartburn among some congressional Democrats, Obama is proposing lower cost-of-living increases for Social Security beneficiaries, employing an inflation index that would have far-reaching consequences, including pushing more people into higher income tax brackets.

Those changes, as well as Obama’s decision not to seek an extension of a temporary payroll tax cut, would force higher tax payments on the middle class, a wide swath of the population that Obama has repeatedly said he wanted to protect from tax increases.

As public posturing has given way to pragmatism, both sides still seem willing to lock in on a substantial agreement rather than just putting off a fiscal day of reckoning. To that end, Obama has conceded that a big bargain would require giving up some of his proposals.

“I understand that I don’t expect the Republicans simply to adopt my budget,” he said during his post-election news conference last month. “That’s not realistic. So, I recognize we’re going to have to compromise.”

The talks, facing a looming deadline, seek to avoid spending cuts at the Pentagon and in domestic programs that are set to kick in at the start of the new year. Economists inside and outside the government have warned that the combination of spending cuts and tax hikes could stall a weak recovery and threaten a new recession.

Despite signs of progress, there are still plenty of disputes to iron out. And people familiar with Obama’s proposal were careful not to describe it as his final offer.

The Obama plan seeks $1.2 trillion in revenue over 10 years and $1.2 trillion in 10-year spending reductions. Boehner aides say the revenue is closer to $1.3 trillion if revenue triggered by the new inflation index is counted, and they say the spending reductions are closer to $930 billion if one discounts about $290 billion in lower estimated debt interest.

“Any movement away from the unrealistic offers the president has made previously is a step in the right direction,” Boehner spokesman Brendan Buck said. “But a proposal that includes $1.3 trillion in revenue for only $930 billion in spending cuts cannot be considered balanced.”

Either way, though, there is no doubt Obama has moved in Boehner’s direction after Boehner opened the door to a tax rate increase.

Obama’s plan, like Boehner’s, would also raise taxes on dividends and capital gains from 15 percent to 20 percent. Both would also reduce the number of deductions and exemptions that wealthy taxpayers can claim. Obama’s proposal also would let estate taxes revert to 55 percent on estates after allowance for a $1 million exemption.

In making his offer, Obama stiff-armed Republican demands to increase the eligibility age for Medicare from 65 to 67, a goal Democrats strongly reject. He also sought to contain cuts in Medicare and other health care programs to about $400 billion over 10 years, less than what Republicans want. And he is continuing to seek spending on unemployment assistance and on public works projects.

Obama’s willingness to reduce future cost-of-living increases in Social Security would also mean smaller annual increases in government pensions and veterans’ benefits. Annual adjustments to income tax brackets would be smaller, pushing more people into higher tax brackets.

Over time, because annual adjustments to the poverty level would be smaller, the new index could reduce the number of people eligible for programs such as Medicaid, Head Start, food stamps, school lunches and home heating assistance.

To avoid some of that risk, Obama wants lower-income recipients to receive protection against any loss from scaling back future cost-of-living increases, people familiar with his plan said.