The NBC/WSJ poll shows that 48 percent of Americans credit Obama with emphasizing unifying themes, compared to 43 percent who say he takes a partisan approach "that does not unify the country." By contrast, Americans by three to one say the Republican Party takes a partisan approach (64 percent) rather than a unifying one (22 percent).
A 49 percent plurality of Americans says the Democratic Party takes a partisan approach, outpacing the 37 percent who says Democrats emphasize unity. But the recently re-elected president's superior ability to attract attention to his message gives his party the edge in casting its approach to the looming March 1 budget "sequester" as one that aims at compromise.
The Republican Party's image problems extend across a wide range of issues. The poll shows Democrats with robust advantages on helping the middle class, handling Medicare, dealing with health care, reducing gun violence, dealing with Social Security and energy policy. Democrats have narrow advantages on several issues that once favored Republicans: immigration, taxes and the economy.
(Read More: White House Immigration Plan Stirs Anger in GOP)
"Republicans don't need a silver lining, they need a whole new playbook," said Fred Yang, one of the NBC/WSJ pollsters.
But Republicans retain a narrow edge on reducing the deficit, and strong advantages on controlling spending and ensuring a strong defense. And even though Obama retains a solid 50 percent job approval rating, the escalating battle in Washington has taken a toll on him, too.
The proportion of Americans who say the nation is headed in the wrong direction has declined to 32 percent from 41 percent in December. But that's hardly a ringing endorsement: Approval for Obama's handling of the economy has declined to 44 percent from 49 percent since January.
The telephone poll of 1,000 adults, conducted by the firms of Democratic pollster Peter Hart and his Republican counterpart Bill McInturff, took place Feb. 21-24. It carries a margin for error of 3.1 percentage points.
—By CNBC's John Harwood; Follow him on Twitter: