While the focus now is on a possible agreement in coming days or weeks, anti-tax crusader Grover Norquist told CNN earlier this week that the nation should gird for long-range battle.

"It's four years of a fight. It's not one week of a fight," said Norquist, who has threatened to mount primary challenges against Republicans who violate a pledge they signed at his behest against ever voting for a tax increase.

While both sides say they want to avoid the fiscal cliff, signs are emerging that a deal would come after the new year to blunt the harshest impacts.

Under that scenario, the new Congress convening in early January would vote to lower taxes from the higher rates that will go into effect in January when the Bush cuts expire, with the new top rates staying intact.

According to a senior administration official, Obama continues to oppose a Republican call for extending the Bush-era tax cuts for everyone to buy time for working out a broader deficit reduction deal that would include overall tax reform.

However, a Senate Republican leadership aide told CNN that Republicans reject Obama's $250,000 threshold for tax cut extensions.

"We're going to be here New Year's Eve," retiring Sen. Joe Lieberman said Sunday on CNN's "State of the Union," adding that it was likely the nation would go over the fiscal cliff.

Failing to meet the year-end deadline on striking a deal would amount to "the most colossal, consequential act of congressional irresponsibility in a long time," said Lieberman, an independent from Connecticut who caucuses with Democrats. "Maybe ever in American history, because of the impact it will have on almost every American."

However, Norquist called the situation part of a longer process, 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.

On Wednesday, Treasury Secretary Timothy Geithner informed Congress that the government would reach its borrowing limit at the end of the year -- in five days' time -- but could take steps to create what he called "headroom" for two months or so.

However, Geithner said uncertainty over the fiscal cliff negotiations and possible changes to the deficit situation made it difficult to predict precisely how long the government's steps to ease the situation would last.

Before heading to Hawaii last Friday, 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, expected to occur on 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 the alternative tax plan pushed by Boehner, their leader.

Reid and other Senate Democrats say House Republicans must accept that agreement will require support from legislators in both parties, rather than a GOP majority in the House pushing through a measure on its own.

He insisted that a Senate-passed plan with Obama's $250,000 threshold would pass the House if Boehner would allow a vote. However, the Senate proposal is held up on constitutional grounds, because legislation that increases revenue must originate in the House.

Boehner and Republicans complain the Senate has refused to take up any proposals they have passed in the past two years. Reid argues that the GOP measures amount to a conservative wish list of unacceptable spending cuts and reforms intended to shrink government and weaken entitlement programs vital to senior citizens, the poor and the disabled.

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.

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.

Obama'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.