Much or all of the revenue to be raised through higher taxes on the wealthy would help hold down the amount paid to the Internal Revenue Service by the middle class.
In addition to preventing higher rates for most, any agreement would retain existing breaks for families with children, for low-earning taxpayers and for those with a child in college.
In addition, the two sides agreed to prevent the Alternative Minimum Tax from expanding to affect an estimated 28 million households for the first time in 2013, with an average increase of more than $3,000. The law was originally designed to make sure millionaires did not escape taxes, but inflation has gradually exposed more and more households with lower earnings to its impact.
To help businesses, the two sides also agreed to extend an existing research and development tax credit as well as other breaks designed to boost renewable energy production. Details on those provisions were sketchy.
Obama's remarks irritated some Republicans.
Sen. John McCain of Arizona said 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.