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The pair will also discuss whether the estate tax should be kept at current low levels or allowed to rise, the aide said.
Democrat Reid warned of tough talks.
“It’s not easy, we’re dealing with big numbers, and some of that stuff we do is somewhat complicated,” he said.
McConnell described Friday’s White House summit, also attended by Democratic House Minority Leader Nancy Pelosi, as “a good meeting.”
“So we’ll be working hard to try to see if we can get there in the next 24 hours. So I’m hopeful and optimistic,” he said.
If things cannot be worked out between the Senate leaders, Obama said he wanted both chambers in Congress to vote on a backup plan that would increase taxes only for households with more than $250,000 of annual income.
The plan would also extend unemployment insurance for about 2 million Americans and set up a framework for a larger deficit reduction deal next year.
There are signs in the options market that investor fear is taking hold. The CBOE Volatility Index, or the VIX, the market’s favored anxiety indicator, has remained at relatively low levels throughout this process, but it moved on Friday above 22, the highest level since June.
But some in the market were resigned to Washington going beyond the New Year’s Day deadline, as long as a serious agreement on deficit reduction comes out of the talks in early January.
“Regardless of whether the government resolves the issues now, any deal can easily be retroactive. We’re not as concerned with January 1 as the market seems to be,” said Richard Weiss, a senior money manager at American Century Investments.
Another component of the “fiscal cliff” - $109 billion in automatic spending cuts to military and domestic programs - is set to kick in on Wednesday.
S&P rating agency said on Friday the fiscal cliff impasse did not affect the U.S. sovereign rating.
That lifted the immediate threat of a downgrade from the agency, which cut the United States’ triple-A rating in August, 2011 in an unprecedented move after a similar partisan budget fight.