"This is not a fight that begins and ends the first week of January," he said, predicting "a regular fight" when Congress needs to authorize more government spending and raise the federal debt ceiling in coming months.
"There the Republicans have a lot of clout because they can say we'll let you run the government for the next month, but you've got to make these reforms," he explained.
Obama spoke separately Friday with Boehner and Reid to try to salvage a fiscal cliff deal by the end of year, then delivered a previously unscheduled statement to reporters at the White House.
He acknowledged what has become obvious: The broader deficit reduction deal he seeks will probably come in stages, rather than in the so-called grand bargain he and Boehner have been trying to negotiate.
In particular, Obama called for Congress to come back after Christmas and work with him on a limited agreement to prevent tax hikes on the middle class, extend unemployment insurance and set a framework for future deficit reduction steps.
Boehner's spokesman said the speaker will be "ready to find a solution that can pass both houses of Congress" when he returns to Washington, as now planned for Thursday.
The GOP opposition to any kind of tax rate increase has stalled deficit negotiations for two years and led to unusual political drama, such as McConnell recently filibustering a proposal he introduced and Thursday night's rebuff by House Republicans of an alternative tax plan pushed by Boehner, their leader.
Boehner said at a news conference Friday that his Republican colleagues refused to back his plan, which would have extended all tax cuts except for income of more than $1 million, because of fears of being blamed for a tax increase.
The negotiations with Obama on a broad deficit reduction agreement hit an impasse last week when both sides offered their "bottom line" positions, Boehner said. In what was considered as progress just a week ago, the president and speaker made major concessions but remained a few hundred billion dollars apart.
Reid and other Senate Democrats say House Republicans must accept that agreement will require support from legislators in both parties. He insisted that the Senate-passed plan with Obama's $250,000 threshold, which polls show is strongly supported by the public, would pass the House if Boehner would allow a vote.
Some House Republicans have said they would join Democrats in supporting the president's proposal in hopes of moving past the volatile issue to focus on the spending cuts and entitlement reforms they seek.
The possibility of a fiscal cliff was set in motion over the past two years as a way to force action on mounting government debt.
Now, legislators risk looking politically cynical by seeking to weaken the measures enacted to try to force them to confront tough questions regarding deficit reduction, such as reforms to popular entitlement programs such as Social Security, Medicare and Medicaid.
Polling has consistently shown most Americans back the president, who insists wealthy Americans must pay more, rather than Boehner and his Republican colleagues, who have balked at tax rate hikes and demanded spending cuts and entitlement program reforms.
A new CNN/ORC International survey last week found that just over half of respondents believe Republicans should give up more in any solution and consider the party's policies too extreme.
The two sides seemingly had made progress early last week on forging a $2 trillion deficit reduction deal that included new revenue sought by Obama and spending cuts and entitlement changes desired by Boehner.
The president's latest offer set $400,000 as the income threshold for a tax rate increase, up from his original plan of $250,000. It also included a new formula for the consumer price index applied to some entitlement benefits, much to the chagrin of liberals.
Called chained CPI, the new formula includes assumptions on consumer habits in response to rising prices, such as seeking cheaper alternatives, and would result in smaller benefit increases in future years.
Statistics supplied by opponents say the change would mean Social Security recipients would get $6,000 less in benefits over the first 15 years of chained CPI.
Liberal groups sought to mount a pressure campaign against including the chained CPI after news emerged this week that Obama was willing to include it, calling the plan a betrayal of senior citizens who had contributed throughout their lives for their benefits.