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Meanwhile, only 38 percent say that such one-party control will be bad, according to the cnn survey.
"That much good will from the public opens a window of opportunity for the Democrats," said Keating Holland, cnn's polling director.
But he warned that the public expects results and may not listen to excuses for very long if a Democratic Congress and White House can't get their act together in time.
The poll also suggests that the public has a positive view of the Democratic Party, with 62 percent having a favorable opinion and 31 percent an unfavorable opinion.
That is not the case for the Republicans, with a majority, 54 percent, having an unfavorable view of the GOP and 38 percent holding a positive view.
"The public has a positive view of the Democratic Party, while the GOP 'brand' is hurting," Holland said. "Overall views of the Democratic Party have gone from 53 percent favorable in October to62 percent favorable now. The GOP overall has seen a five-point drop in its favorable rating."
The 62-percent figure is the "the highest opinion of the Democrats in at least 16 years, since before Bill Clinton got elected," said Bill Schneider, a political analyst.
The poll indicates that the public is split regarding top Democrats in Congress -- but that's an improvement.
On the Nov. 4 election day, the Democrats not only won the presidency, but also increased their majority status in Congress.
With Senate contests in Alaska, Georgia and Minnesota still unresolved, the Democrats have increased from 51 seats to 57 in the chamber.
In the House of Representatives, the Democrats have picked up 20 seats, to 255, with six races still undecided.
The cnn poll was conducted Thursday through Sunday, with 1,246 adult Americans questioned by telephone.