Americans overwhelmingly want President Obama and both parties in Congress to work toward compromise on major issues in the next two years, a new poll suggested Thursday.

Nearly three-quarters of U.S. adults urged the president, along with congressional Democrats and Republicans, to show flexibility on their positions, though party leaders have shown little willingness to do so.

Sixty-nine percent of adults said Obama should compromise on some of his positions in order to get more done, according to a New York Times/CBS News poll. Seventy-six percent of adults said the same of congressional Democrats, while 78 percent of Americans said that congressional Republicans, who are poised to potentially retake control of the House, should look for common ground. 

The public's desire for compromise was underscored further by a second poll on Thursday. Eighty percent of likely voters said in a new Bloomberg National Poll that the two parties should work together in the next two years, if the GOP takes control of one or both chambers. Sixteen percent of likely voters said that Republicans and Democrats should stick to their principles, even if it means gridlock.

The public's desire for compromise contrasts plenty with what political leaders have said about the two parties' ability to work with each other. Even though Republicans look well-positioned to control the House over the next two years, its leaders have not seemed eager to compromise.

"This is not a time for compromise, and I can tell you that we will not compromise on our principles," said House Minority Leader John Boehner (R-Ohio), who would likely become Speaker under a GOP majority, on Wednesday afternoon. That came after other Republicans vowed no compromise last week on major issues, too.

Obama's said that he welcomes compromise and would look to find some with Republicans —within reason.

"I’m just going to keep on trying to see where they want to move the country forward," the president told a group of liberal bloggers on Wednesday. "But I don’t go into the next two years assuming that there’s just going to be gridlock."

The NYT/CBS poll, conducted Oct. 21-26, has a 3 percent margin of error. The Bloomberg poll, conducted Oct. 24-26, has a 3.1 percent margin of error.

—Updated 6:58 a.m.