President Barack Obama says it appears that an agreement to avoid the fiscal cliff is “in sight,” but says it’s not yet complete and work continues.

Obama says this has been a “pressing issue on people’s minds,” and tells an audience of middle-class taxpayers the deal would, among other things, extend unemployment benefits for Americans “who are still out there looking for a job.”

He voiced regret that the work of the administration and lawmakers on Capitol Hill won’t produce a “grand bargain” on tax-and-spend issues, but said that “with this Congress, it couldn’t happen at that time.”

Officials familiar with the negotiations say an agreement would raise tax rates on family income over $450,000 a year and increase the estate tax rate.

Any overall deal was also likely to include a provision to prevent a spike in milk prices with the new year, extend unemployment benefits due to expire and protect doctors who treat Medicare patients from a 27 percent cut in fees.

Both the House and Senate were on track to meet on the final day of the year, although there was no expectation that a compromise could be approved by both houses by midnight, even if one were agreed to.

Instead, the hope of the White House and lawmakers was to seal an agreement, enact it and send it to Obama for his signature before taxpayers felt the impact of higher income taxes or federal agencies began issuing furloughs or taking other steps required by spending cuts.

Regardless of the fate of the negotiations, it appeared all workers would experience a cut in their-home pay with the expiration of a two-year cut in payroll taxes.

Officials who described the negotiations did so on condition of anonymity, citing the confidential nature of the discussions.

A spokesman for McConnell, Don Stewart, said the Kentucky lawmaker and Biden “continued their discussion late into the evening and will continue to work toward a solution.” Underscoring the flurry of activity, another GOP aide said the two men had conversations at 12:45 a.m. and 6:30 a.m. Monday.

Unless an agreement is reached and approved by Congress by the start of New Year’s Day, more than $500 billion in 2013 tax increases will begin to take effect and $109 billion will be carved from defense and domestic programs

Though the tax hikes and budget cuts would be felt gradually, economists warn that if allowed to fully take hold, their combined impact — the so-called fiscal cliff — would rekindle a recession.

“This whole thing is a national embarrassment,” Sen. Bob Corker, R-Tenn., said Monday on MSNBC, adding that any solution Congress would swallow at this late stage would be inconsequential. “We still haven’t moved any closer to solving our nation’s problems.”

In a move that was sure to irritate Republicans, Reid was planning — absent a deal — to force a Senate vote Monday on Obama’s campaign-season proposal to continue expiring tax cuts for all but those with income exceeding $200,000 for individuals and $250,000 for couples.

In one sign of movement on Sunday, Republicans dropped a demand to slow the growth of Social Security and other benefits by changing how those payments are increased each year to allow for inflation.

Obama had offered to include that change, despite opposition by many Democrats, as part of earlier, failed bargaining with House Speaker John Boehner, R-Ohio, over a larger deficit reduction agreement. But Democrats said they would never include the new inflation formula in the smaller deal now being sought to forestall wide-ranging tax boosts and budget cuts, and Republicans relented.

“It’s just acknowledging the reality,” Sen. Susan Collins, R-Maine, said of the GOP decision to drop the idea.

There was still no final agreement on the income level above which decade-old income tax cuts would be allowed to expire. While Obama has long insisted on letting the top 35 percent tax rate rise to 39.6 percent on earnings over $250,000, he’d agreed to boost that level to $400,000 in his talks with Boehner. GOP senators said they wanted the figure hoisted to at least that level.

Senators said disagreements remained over taxing large inherited estates. Republicans want the tax left at its current 35 percent, with the first $5.1 million excluded, while Democrats want the rate increased to 45 percent with a smaller exclusion.

The two sides were also apart on how to keep the alternative minimum tax from raising the tax bills of nearly 30 million middle-income families and how to extend tax breaks for research by business and other activities.