McConnell told CNN Friday the two leaders hoped to have a plan they could bring to their caucuses Sunday.
Most of the actual discussions would be done by the two senators' staffs, their aides said, and carried on by email and telephone.
President Barack Obama and congressional Democrats would like to bring in more revenue by raising income tax rates for income above $250,000, while preserving current rates for all income under $250,000. Republicans apparently hope to increase the limit to $400,000 and would also like to keep estate taxes low.
In his weekly radio talk, Obama urged Congress, if no deal is in place, to pass legislation extending tax cuts for those with incomes under $250,000, and to extend long-term unemployment insurance benefits.
If no budget deal is in place by Jan. 1, the tax cuts passed under President George W. Bush would end and automatic across-the-board cuts in federal spending would kick in -- creating what has come to be called the fiscal cliff.
House Republican leaders said they were considering calling a hearing for Rules Committee Sunday to establish rules for a possible vote on a bipartisan deal.
Rules Committee Chairman David Dreier of California told Roll Call, "We've been working, and we're ready to go as soon as we come up with something."
The budget deal is likely to include many issues besides tax rates, including the alternative minimum tax, and House Republican leaders have notified members votes may be held through Jan. 3, Roll Call reported.
Dreier said House Speaker John Boehner, R-Ohio, and other Republicans officials would need time to review any agreement Reid and McConnell are able to get through the Senate.
U.S. drone attack in Pakistan kills 4
GURBUZ, Pakistan, Dec. 29 (UPI) -- A U.S. drone attack in North Waziristan, Pakistan, resulted in the deaths of four suspected militants, officials said.
The Friday attack targeted a house in the town of Gurbuz, in the border area of North and South Waziristan, Khaama Press reported. The exact target of the strike has not been disclosed.
"The drones fired two missiles on a house believed to be a militant center. Four militants were killed and two injured," a security official said, adding that no senior al-Qaida members or allied jihadist were killed in the attack.
The United States has carried out 46 drone attacks in North Waziristan in 2012, down from 72 strikes in 2011.
Bus explosion in Karachi kills six
KARACHI, Pakistan, Dec. 29 (UPI) -- Six people were killed Saturday when a bus exploded outside the main railway station in Pakistan's largest city, Karachi, authorities said.
About 50 people were reported injured, some of them critically, Dawn News reported.
Ahmed Chinoy, head of the Citizen Police Liaison Committee, said investigators were unsure whether the blast was a terrorist act or an accident, possibly from an exploding natural gas cylinder.
The bus was parked outside the Karachi Cantonment Railway Station when it exploded with such force its roof was blown off.
The area is a hub for travel locally and to other cities in Pakistan.
Fresh snow falls in U.S. Northeast
INDIANAPOLIS, Dec. 29 (UPI) -- Parts of the Midwest were reporting 4-5 inches of new snow Saturday as a hefty winter storm headed toward the U.S. East Coast, forecasters said.
The storm was blamed for at least 10 deaths nationwide this week.
Flightstats.com said more than U.S. 400 flights were canceled and about 5,000 had been delayed Saturday. More than 110 of the cancellations were at Newark Liberty International, about 80 were at New York's La Guardia Airport and almost 60 were at JFK International Airport.
WMUR-TV, Manchester, N.H., reported several people were injured in a chain-reaction crash involving an estimated 20 vehicles amid snow and freezing temperatures on Interstate 93 in New Hampton Saturday.
New York state highway officials said several highways were closed across the state because of snow-related collisions.
Accuweather.com said the heaviest snowband at 5 p.m. EST Saturday extended from Oxford and Hartford, Conn., to Worcester and Bedford, Mass.
Holly, Vt., had 7 inches of snow by late Saturday afternoon, while Pittsford, Vt., had 6.5 inches, and Killington had 6.1 inches.
AccuWeather said 5.1 inches was on the ground in the Indianapolis suburbs and Columbus, Ohio, checked in with 4 inches. New York and Pittsburgh were expecting at least a couple of inches Saturday.
"It will keep the ski resorts happy and they won't waste money making snow," said John Goff, lead forecaster for the National Weather Service office in Burlington, Vt., told CNN.
The National Oceanic and Atmospheric Administration said a survey of the lower 48 states found snow covered 64 percent of the total area -- a degree of coverage meteorologists told CNN was not seen last winter until February.
"Our current snow cover is not anything unusual," AccuWeather's Jack Boston said. "It was just way less than normal last winter."