President Obama: 'Fiscal cliff' deal 'in sight,' not done (+ video)
Obama's remarks irritated some Republicans.
Sen. John McCain of Arizona they would "clearly antagonize members of the House."
There was no response from Speaker John Boehner, who has been content to remain in the background while McConnell did the negotiating.
Some Democratic officials said that with his comments, Obama was hoping to ease the concerns of liberals in his own party who feared he had given away too much in the current round of talks over taxes.
Obama campaigned on a call for higher tax rates on income over $200,000 for individuals and $250,000 for couples, far lower than the $400,000 and $450,000 that Biden and McConnell have set.
Similarly, the pending agreement on the estate tax would allow more large estates to escape taxation than many Democrats prefer.
By late afternoon, the two sides remained separated by a stubborn dispute over spending cuts scheduled to take effect on the Pentagon and domestic programs alike.
Officials familiar with the talks said the White House has been seeking agreement to stop the cuts from taking effect, either for a period of months or a year, and wanted to count higher taxes created elsewhere in the legislation to offset the cost.
Republicans have said they are willing to delay the across-the-board cuts, but only if Obama and Democrats agree to targeted savings from government programs to take their place.
Associated Press writers Andrew Taylor, Alan Fram and Ben Feller contributed to this report.
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