With liberal leaders grumbling about what they see as President Obama’s failure to hold firm in the recent debt ceiling talks and other decisions, one critical player — MoveOn.org — is still deciding whether to mobilize for his campaign.

“We are all incredibly frustrated,” said Justin Ruben, MoveOn’s executive director.

That frustration, over compromises in economic and environmental policy, could turn into a deflated reelection effort by the influential left-wing group’s members, nearly 1 million of whom volunteered for his campaign in 2008 and gave $88 million.

“Republicans will begin with an advantage,” said Thomas Mann, a political scholar at the Brookings Institution. “Obama is going to have to work very hard and build an extensive grass-roots effort.”

This month, the group’s long list of grievances with the White House grew when Obama backed off a proposal to toughen the country’s smog regulations. Ruben said that played into what his members see as a narrative of capitulation, and it has left him wondering whether they will hit the streets again to try to reelect the president. They are also upset about the president’s failure to carry out a campaign promise to close the prison at Guantanamo Bay, Cuba.

MoveOn, which was formed in 1998 in response to the impeachment effort against President Clinton, was one of the first big liberal groups to back Obama in 2007. Its leaders and members mobilized to encourage others to back him.

“I don’t think [opposition to] Rick Perry or Mitt Romney will be enough to incite the kind of passion that Obama needs to win,” said Ruben, described by many of his members as bitterly disappointed in Obama. “In 2010, progressives were not impassioned, and we saw what happened.”

Obama campaign officials have rejected descriptions of wholesale disenchantment on the left, but they are following a two-pronged strategy: Play down the disappointment in the media, and pay added attention to the groups that are complaining. In a memo Friday, senior strategist David Axelrod said Obama’s support among key groups remains solid.

“Despite what you hear in elite commentary, the president’s support among base voters and in key demographic groups has stayed strong,” he said. “The base is mobilized behind the president.”

Axelrod also pointed to polls showing relatively high approval ratings for Obama among liberals. In the latest Washington Post-ABC News poll, 69 percent of liberals said they approved of the president. A campaign spokeswoman also cited the 12,000 people who signed up for the campaign’s summer fellows program and the more than half-million who gave to the campaign in the second quarter. Nearly half of those donors had never given to Obama before, she said.

The campaign also recently launched Operation Vote, its organizing and outreach initiative focused on energizing its base through advertising, online networks and voter registration efforts.

The extra focus could be necessary to reach people such as Serena Zhao, an environmental activist and senior at Harvard University. In 2008, she went to New Hampshire to canvas for Obama and help get out the vote. This month, she stood outside a dormitory on campus to protest a visit by Jim Messina, Obama’s campaign manager. She and other students held signs that said “President Obama, Yes You Can. Stop the Keystone XL Pipeline,” referring to a controversial oil pipeline opposed by environmental groups.

“There’s been a feeling of betrayal,” Zhao said. “That word has been tossed around a lot.”

She plans to vote for Obama, but “it’s just a matter of us getting over the disappointment to go out and get on the streets again.”

Tim Brown, who leads a group of MoveOn members outside of Philadelphia, said he is looking to see how hard Obama pushes on the jobs bill he has put before Congress. Brown was laid off from a six-figure job two years ago and says Democrats “need to fight.”

“Time and time again I have seen [Obama] compromising with tea party representatives on core Democratic principles,” he said. “Am I going to show up and knock on doors? You bet I am, but we need to push Obama in the right direction.”

Griffin Bunnell, a 25-year-old MoveOn member in Houston, is more understanding, saying Obama is in a tough situation.

“If he gets reelected in 2012, he won’t have to be worried about being reelected again,” Bunnell said. “Right now, he has to bend and break because of all of the obstructionists in Congress.”

Eventually, most MoveOn.org members will probably be persuaded to get behind Obama, Mann said.

“I don’t believe they will be on the sidelines,” he said. Obama, he said, must “try to create a sense of fear amongst those on the left about what could happen if Republicans control” Congress and the White House.

Polling analyst Peyton Craighill contributed to this report.