Boehner said a vote on a Republican bill along these lines could come as early as this week in the House.
Obama could face unrest from rank and file fellow Democrats. Liberal Democrats are likely to oppose a key compromise he has offered to permit shrinking cost-of-living increases for all but the most vulnerable beneficiaries of the Social Security retirement program.
The president's proposal calls for using a different formula, known as "chained Consumer Price Index," to determine the regular cost-of-living increases and essentially reduces benefits.
Obama on Monday conceded allowing the extension of low income tax rates begun during the Bush administration for incomes up to $400,000 per household. He had previously insisted setting that cut-off at $250,000.
Boehner had earlier conceded to agreeing that Bush-era tax rates can expire for the wealthiest Americans, after opposing for months tax rate increases of any kind. He proposed setting a $1 million income threshold for raising rates.
Some analysts expect a compromise could come at $500,000. "That still looks like a safe bet," said Greg Valliere, chief political strategist at Potomac Research Group.
Obama also moved closer to Boehner on the proportion of a 10-year deficit reduction package that should come from increased revenue, as opposed to cuts in government spending. Obama is now willing to accept a revenue figure of $1.2 trillion, down from his previous $1.4 trillion proposal.
Boehner's latest proposal calls for $1 trillion in new tax revenue from higher tax rates and the curbing of some tax deductions taken by high-income Americans.
Missing from Obama's latest offer was any extension of the so-called "payroll tax holiday" that ends on Jan. 1, bringing an immediate tax increase on wage earners.
A Republican aide who asked not to be identified said that "conceptually" there was agreement to make permanent changes in the tax code, with some of those changes taking effect at the start of 2013 and others at the beginning of 2014.
A thorough cliff-avoiding agreement could immediately substitute more targeted spending cuts for the indiscriminate slashing of programs known as "sequestration."
Possible plans to produce cuts in spending for Medicare and Medicaid, the government health insurance programs for seniors and low-income Americans respectively, remained to be discussed.
Boehner and Obama have made headway on the politically explosive question of the president's ability to avoid constant battles over raising the nation's debt ceiling, which controls the level of borrowing by the government. Boehner is ready to give Obama a year of relative immunity from conservative strife over the debt ceiling, while Obama is pushing for two years.