WASHINGTON - When California Gov. Arnold Schwarzenegger nabbed an endorsement from Common Cause for his plan to redraw political district lines, some Democrats and open-government activists were dismayed.

How could the respected good government group sign on with a governor who’s been criticized for his supercharged fund-raising? Why was Common Cause embracing a plan that’s picked up little or no backing from other nonprofit groups?

“Common Cause is star-struck and so they’re lending the governor their brand,” said Jamie Court, president of the Foundation for Taxpayer and Consumer Rights, a Santa Monica-based consumer group that’s among Schwarzenegger’s chief critics. “They’ve given him more credibility than he deserves for a plan that is clearly a power grab.”

But like many political relationships, the endorsement was, in part, a marriage of convenience. Schwarzenegger got what amounted to a Good Housekeeping seal of approval for his proposal, and Common Cause got a high-profile advocate for a key issue that can be hard to put in the spotlight _ nonpartisan redistricting.

“We are all looking for ways to put the important issues we care about more squarely in the public dialogue, and it doesn’t mean that every time we get all the policy we want out of that,” said Chellie Pingree, Common Cause’s president. “But we go behind the scenes and work in the state legislatures, or at the referendum level, or with our citizen activists, to move the debate when the public is paying attention.”

The plan, endorsed by Common Cause at a joint Washington press conference with Schwarzenegger on Thursday, would take the job of drawing congressional and state legislative district boundaries away from lawmakers and give it to a panel of retired judges. The redistricting would happen next year, instead of after the 2010 census, which would be the normal timeline.

Schwarzenegger believes the plan would lead to more competitive districts and to lawmakers who better represent voters. The way district lines are currently drawn in California protects incumbents _ of 153 state legislative and congressional seats up for grabs in November, none changed party hands.

Members of both political parties have concerns about the plan. Republicans fear redrawing district lines in Democrat-leaning California could cost the party House seats. Democrats suspect Schwarzenegger’s motives because of the example of Texas, where a GOP redistricting plan cost four Democrats their seats in November.

Advocacy groups have different reasons for not signing on to Schwarzenegger’s proposal.

Groups including the Mexican American Legal Defense and Educational Fund, the Center for Governmental Studies in Los Angeles, and FairVote in Takoma Park, Md., all have problems with the plan. Among them: redistricting should happen only every 10 years and Schwarzenegger’s plan doesn’t adequately provide for competitive districts with diverse voters.

Common Cause endorsed the plan only after Schwarzenegger and the proposal’s author, Assembly Republican Leader Kevin McCarthy, agreed to amendments including expanding the panel of retired judges and establishing diversity as a criteria for selecting the judges.

The changes were enough for Common Cause to decide Schwarzenegger’s plan was good enough to go with.

“We work toward what’s possible and what has the momentum to pass,” Pingree said.

It’s a decision other groups so far haven’t made.

“The tricky thing for groups that have long worked on redistricting is that, in principle, many of the groups agree with the governor’s objectives,” said Kim Alexander, president of the California Voter Foundation. “But the particular plan that he’s outlined for how he wants to meet those objectives is problematic for some of those folks.”

Common Cause officials said they had no problem joining with Schwarzenegger, even though not everything he does is to their liking. The group’s California chapter is even considering submitting a friend of the court brief to support the state’s Fair Political Practices Commission, which is being sued by allies of the governor who want him to be able to raise unlimited amounts of money for ballot initiatives.

The apparent contradiction doesn’t trouble Pingree.

“We’re well-known at times for criticizing and supporting the same person on the same day,” she said. “That’s who we are.”