No one anticipates a stalemate lasting that long, but many experts worry that even allowing the spending cuts and tax increases for a relatively brief period could rattle financial markets.
From their public statements, Obama and Boehner appear at an impasse over raising the two top tax rates from 33 percent and 35 percent to 36 percent and 39.6 percent. Democrats seem confident that Boehner ultimately will have to crumble, but Obama has a lot at stake as well, including a clear agenda for priorities like an overhaul of the nation's immigration laws.
Obama is also meeting privately Thursday with his defeated Republican rival Mitt Romney. The president has cast his victory over Romney as a sign that Americans back his tax proposals, which were a centerpiece of his re-election campaign.
While in Washington, Romney will also meet with his former running mate, Ryan. The Wisconsin congressman is chairman of the House Budget Committee and deeply involved in the fiscal cliff discussions.