Most Democrats don't wish to see President Obama face a primary challenge in 2012, according to a new poll released Wednesday.

Despite frustration among liberals that the president has ceded too much ground to congressional Republicans on the debt ceiling and on other major issues, just 32 percent of Democrats and Democratic-leaning Independents wish to see a primary challenge to the president.

Fifty-nine percent of Democrats said they would not wish to see a challenge to Obama, according to a Pew Research Center/Washington Post poll conducted after the recent debt-ceiling deal. The president agreed to a compromise bill that included only spending cuts and none of the revenue increases on which he had insisted.

Sen. Bernie SandersBernard (Bernie) SandersOvernight Defense: Senate passes 0B defense bill | 3,000 US troops heading to Afghanistan | Two more Navy officials fired over ship collisions Senate passes 0B defense bill Dems fear lasting damage from Clinton-Sanders fight MORE (I-Vt.), a liberal stalwart, suggested at the height of the battle in Congress over that deal that a primary to Obama would be a "good thing." Consumer activist Ralph Nader has said he's recruiting candidates to run against Obama in different key primary states.

But even self-described liberals aren't much different in thinking Obama deserves a primary challenge. Thirty-three percent of liberals support a primary challenge to the president, while 62 percent oppose such a maneuver.

The poll, conducted Aug. 4-7, has a 4 percent margin of error.

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