Call this week’s election a political mulligan — a new opportunity for divided, dysfunctional government to find a compromise on tax increases, spending cuts, debt and a mediocre economy.

Politicians in both parties Wednesday said they hope to find common ground on a range of pressing challenges — while conceding that voters did little to break the partisan gridlock that has gripped ever tighter on the country’s levers of power.

Final election returns showed Republicans kept their hold on the U.S. House. Democrats picked up seats in the Senate. President Barack Obama will stay in the White House.

Despite that more-of-the-same formula, some actually saw a glimmer of a shot at change.

“Over 80 percent of the people coming out of the polls said, ‘Work this out. Don’t be rigid,’ ” said Dan Glickman, former agriculture secretary and Kansas congressman, and now a fellow at the Bipartisan Policy Center in Washington. “That message has got to get through.”

Republican and Democratic leaders made similar, possibly wishful, statements.

“This country is not saying to either party, ‘You’re 100 percent right,’ ” said Sen. Claire McCaskill, the Missouri Democrat who was easily re-elected Tuesday. “We need to … come together and quit fooling around.”

McCaskill said she discussed the issue with Obama Wednesday. The re-elected chief executive also phoned leaders of both parties in Congress.

“Compromise is not a dirty word,” said Senate Majority Leader Harry Reid, a Nevada Democrat. “It’s better to dance than to fight.”

House Speaker John Boehner, an Ohio Republican, also talked of “creating an atmosphere” for common ground.

Senate Minority Leader Mitch McConnell of Kentucky joined in, sort of. “To the extent (the president) wants to move to the political center, which is where the work gets done in a divided government, we’ll be there to meet him halfway,” he said in a statement that seemed to emphasize that it was Obama who needed to start giving in.

Others, though, said the voters’ endorsement of the political status quo did little to fully settle quarrelsome issues like raising tax rates or cutting entitlement programs such as Medicare and Social Security.

The issues — and most of the faces — are the same after the voting as they were before.

“It’s confusing,” said U.S. Rep. Kevin Yoder, a re-elected Kansas Republican. “The public’s very upset with the status quo, but sent many of the same status quo people back to Washington.”

Stock indexes dropped sharply Wednesday, and partisans from the left and right darkly warned against compromising “principle.”

“If the president offers a serious reform of entitlements, or some other worthwhile policy, conservatives should be willing to bargain with him,” wrote the editors at the National Review, a leading conservative publication. “If he continues on the path of his first term — and why would he not, after this election? — we should feel duty-bound to oppose him.”

Woody Cozad, former chairman of the Missouri Republican Party, said the path forward is murky.

“I’m not very hopeful,” he said. “And I’m sick and tired of the Republicans being blamed for it.”