King is favored to win the three-way race for Snowe's seat.
A Bloomberg poll in September found that 55 percent of Americans said Congress will continue to be an impediment no matter who is elected president. Just 32 percent said Congress would get the message and work together.
Democratic strategist Steve McMahon said he worries that with a divided Congress "we can probably expect hyper partisanship and gridlock everywhere. It seems like Americans can expect more of the same."
The other certainty is neither Obama nor Romney will have much of a mandate based on the razor-thin presidential race and the likelihood that the majority party in the Senate will be nowhere near a filibuster-proof majority.
"Neither candidate will be able to claim that voters endorsed a clear and specific plan for balancing the budget because neither of them offered such a plan," said John J. Pitney, a professor of American politics at Claremont McKenna College.
Republican strategist Terry Holt said a newly elected president who has the will could put their mark on policy and make some significant changes.
"But there is so much ideological division that you will have to risk your political life to get something done in the next Congress," Holt said. "It is an all-or-nothing proposition by virtue of the divided nature of the country. You have to stick your neck out if you're to get anything done."
Weeks before the January inauguration, Congress will have to decide what to do about a $607 billion so-called fiscal cliff: the combination of expiring Bush-era tax cuts and automatic, across-the-board spending reductions to domestic and defense programs. Economists warn that no action will plunge the country into another recession.
"At the end of the day, you have so many ticking time bombs," said GOP strategist John Feehery. "Having just a complete gridlock is not an acceptable solution."
Congress may decide in the lame-duck session to delay the major decisions to early next year, especially if Romney wins the presidency. But they can't put off economic decisions for too long.
"The road to fiscal perdition is a cul-de-sac," Pitney said.
Associated Press writers Andrew Miga and Henry C. Jackson contributed to this report.