The possible makings of a deal could borrow heavily from a near-bargain last year during debt-limit negotiations.
Then, Obama was willing to reduce cost-of-living increases for federal Social Security pension beneficiaries and increase the eligibility age for Medicare, as Boehner and other top Republicans have demanded. On Tuesday, Obama did not shut the door on Republican ideas on such entitlement programs.
"I'm prepared to make some tough decisions on some of these issues," Obama said, "but I can't ask folks who are, you know, middle class seniors who are on Medicare, young people who are trying to get student loans to go to college, I can't ask them to sacrifice and not ask anything of higher income folks."
"I'm happy to entertain other ideas that the Republicans may present," he added in an interview with Bloomberg Television.
At the core, the negotiations center on three key points: whether tax rates for upper income taxpayers should go up, how deeply to cut spending on entitlements such as Medicare and how to deal with raising the government's borrowing limit early next year.
White House spokesman Jay Carney dismissed Boehner's proposals as "magic beans and fairy dust."
Boehner countered: "If the president really wants to avoid sending the economy over the fiscal cliff, he has done nothing to demonstrate it."
Tax rates have emerged as one of the most intractable issues, with Obama insisting the rates on the top 2 percent of earners must go up and Boehner standing steadfast that they must not.
Boehner, instead, has proposed raising $800 billion through unspecified loophole closings and limits on tax deductions.
On Tuesday, the president said he would consider lowering rates for the top 2 percent of earners — next year, not now — as part of a broader tax overhaul effort that would close loopholes, limit deductions and find other sources of government revenue. "It's possible that we may be able to lower rates by broadening the base at that point," Obama said.
On Medicare and Social Security, the Republican proposals would do relatively little to curb the deficit over the next decade, but the impact would grow over the longer term.