The Congressional Progressive Caucus, frustrated by its inability to influence the Democrats’ agenda over the past two years, is considering a new strategy for the 112th Congress that includes changing its leadership structure.

The liberal bloc is co-chaired by Reps. Raúl Grijalva and Lynn Woolsey. Woolsey, who is nearing the end of her sixth year as a leader of the 83-member group, said in a recent interview that she is not ready to say whether she wants to seek another two-year term, but she said she thinks the CPC would function better with just one Member at the helm.

“It’s very complicated to have two chairs,” the California Democrat said.

Although sources said Woolsey and Grijalva do not always get along, they have kept their disagreements private, and Woolsey stressed that her preference for a single CPC chair simply reflects the fact that the group has matured. The CPC is approaching its 20th anniversary.

“Now the caucus is pretty adult, so maybe they can go ahead with one chair,” she said.

Grijalva, who beat out Rep. Keith Ellison for the co-chairman post two years ago when Rep. Barbara Lee (D-Calif.) stepped down to lead the Congressional Black Caucus, said he thought the two-leader system had worked well. But the Arizona Democrat acknowledged that some CPC members are making the case that the group “would not get into any divided decision-making issues” with one chairman.

Ellison, one of the CPC’s seven vice chairmen, said Wednesday he would be interested in moving up the leadership ladder if a spot opened up. “I am going to serve the organization in whatever capacity the members want me to serve in,” the Minnesota Democrat said.

For his part, Grijalva said he wanted another term atop the liberal organization. He said Wednesday that he thinks the CPC has become a force within the larger Caucus, though “not as much as we want or need.”

“But that’s going to come,” he added.

The liberal Democrats tried to wield influence over major debates during the 111th, but had mixed success.

During the debate over health care reform, CPC members threatened to vote against any bill that did not include a public option. But they capitulated, and in March all of them voted in favor of a final version of the health care bill that did not include the public option.

And many liberals were frustrated in November when Democratic leaders gave in to a small group of moderates, led by Rep. Bart Stupak (D-Mich.), and agreed to allow a floor vote on an amendment to the health care bill that barred government-subsidized insurance plans from covering abortions. The language was approved, and a version of the Stupak amendment made it into the final health care law.

Liberals’ inability to match moderates’ influence on health care reform — despite their larger numbers — prompted the CPC to enlist the help of outside grass-roots organizations, such as the Progressive Change Campaign Committee and the recently formed P Street Project.

Strengthening the relationship with those groups is among Grijalva’s top goals for the CPC in the coming months, he said, adding that grass-roots organizations “can become a very effective arm” to try to influence legislation.

Ellison said the groups can be incredibly helpful, saying: “We often find ourselves in a position where we’re looking for leverage. But the leverage we have is the progressive community.”

The outside groups were instrumental in getting Senators to publicly support Elizabeth Warren, the liberals’ pick to head the newly formed Consumer Financial Protection Bureau. President Barack Obama instead picked Warren to serve as an adviser to the new consumer agency.

Grijalva also said the groups have helped the CPC collect 70 signatures for a letter urging the president’s deficit commission to take cuts to Social Security off the table.

Grijalva said “the Progressive Caucus needs to be positioned to play an even bigger role” next Congress, when the GOP is expected to make significant gains. He described the upcoming debate over the deficit commission’s recommendations, slated to be released after the November elections, as one of the “biggest fights” on the horizon for the CPC.

Progressive Change Campaign Committee co-founder Adam Green said Wednesday that groups like his could help the CPC apply pressure and support for liberal Members on their top priorities.

“The tough part is actually getting them to stand their ground on their position,” he said. “It can be a very lonely feeling to challenge leadership. And therefore there’s a role for the grass roots in getting the backs of Members that are willing to stand their ground.”