Both sides are relying on teams of negotiators to work behind the scenes to find common ground.
Obama has tapped Treasury Secretary Tim Geithner as lead negotiator in the talks to avoid going over the "fiscal cliff," sources told ABC News. Other members of the White House economic team are said to play "leading roles," including chief of staff Jack Lew, National Economic Council director Gene Sperling and legislative affairs director Rob Nabors.
Republicans have not publicly designated a team of negotiators. But Boehner has begun meeting daily with key players in approving any future fiscal legislation -- Rep. Dave Camp who chairs the powerful Ways and Means Committee; Rep. Fred Upton who chairs the Energy and Commerce Committee; and Rep. Paul Ryan, the former vice presidential nominee who chairs the Budget Committee.
"We know what the parameters of a deal look like," Carney said. "We know what the substance beneath the parameters of the deal look like. And we are working, as we speak, with our counterparts on Capitol Hill to try to reach that goal."
Some Republican lawmakers echoed that sentiment today, arguing that the negotiations at hand are not as complicated or as nuanced as they may seem.
"We have plenty of time to make these decisions. It's just a matter of doing it. If we can do it in two or three weeks, candidly, they can be made in two to three days," Republican Sen. Bob Corker of Tennessee said on MSNBC.
McConnell urged Obama to take the lead in the coming days. "The only person in America who can really make or break it is the president himself," he said. "He's the only one who can lead his party to do something they wouldn't ordinarily do, to do what's actually needed now, and that's why he's the one who has to present a plan for success."
Meanwhile, both sides of the tax spat continue to court key constituencies to help leverage popular support in their favor.
Boehner and House Republican leaders will meet with former Clinton White House chief of staff Erskine Bowles and members of the so-called 'Fix the Debt' coalition on Wednesday, his office said.
Senior administration officials continue to hold meetings with independent groups on support for letting the Bush-era tax cuts expire on the wealthy. Lew, Sperling and OMB Director Jeff Zients met separately today with U.S. Chamber of Commerce president Tom Donohue.
Obama is expected to hit the road in the coming days to rally voter support for his plan of extending lower tax rates on the middle class while hiking rates on the rich. Obama will host 15 small business owners at the White House for a private meeting and the National Economic Council will release a report on the impact of middle class tax cuts on small businesses.
The push continues Wednesday with Obama playing host to Americans who wrote to the administration online on the importance of extending the tax cuts. He will also hold a second private meeting with business leaders.
The president caps the week with a trip to a Pennsylvania factory that makes K'NEX brand toys to underscore the importance of extending lower tax rates on consumer confidence and purchasing power.
ABC News' Z. Byron Wolf contributed to this report.