Even as he strives to repair the GOP’s battered image with voters and hold together a fractious conference, Eric Cantor, 50, is also trying to remain the heir apparent to Speaker John A. Boehner. (Melina Mara/The Washington Post)

Every week, Eric Cantor huddles in a Capitol Hill basement meeting room with House conservatives, seeking their input on legislation. As House majority leader, he has been a trusted liaison between those activists and the Republican leadership.

Yet in recent days, Cantor (Va.) has begun laying out a far more centrist agenda than the one espoused by the core conservatives who have long formed his power base.

Putting aside his past emphasis on broad cuts to federal programs, he has become an advocate for research on pediatric cancer, passing legislation that would increase funding for the National Institutes of Health.

Cantor has begun talking about urban poverty, visiting charter schools to explore education reform, and has sought alliances with African American lawmakers, traveling to Mississippi to appear at a civil rights event and honor Rep. John Lewis (D-Ga.).

And he has maneuvered behind the scenes to push House Republicans toward an eventual floor vote on a plan to legalize certain illegal immigrants who were brought to the United States as children.

The shift, which has rankled some House conservatives, underscores the political challenge confronting Cantor in the lead-up to this year’s midterm elections. Even as he strives to repair the GOP’s battered image with voters and hold together a fractious conference, Cantor, 50, is trying to remain the heir apparent to Speaker John A. Boehner (R-Ohio).

Each move and gesture seems designed to nudge conservatives toward a more even-tempered message, but Cantor resists challenging his party’s ideology or platform, knowing he can go only so far and remain the presumptive favorite among House Republicans for the speaker’s gavel should Boehner, 64, decide to retire in the coming years.

“The growing realization around here is that the differences [between the parties] are still there, but that doesn’t mean we can’t focus on the things that bring us together,” Cantor said in an interview. “The public is looking for someone who has their back.”

Cantor’s task is daunting. Recent polls show that only about one voter in five has confidence in House Republicans.

Meanwhile, a handful of conservative members have expressed their disapproval of the new strategy, particularly given that its architect is a man they considered a fellow partisan warrior. Cantor, after all, drew praise from the right during budget talks for his tense encounters with President Obama. Randolph-Macon College economics professor David Brat, a tea party candidate challenging Cantor in his district, has alluded to the majority leader’s evolving pitch, calling him an “Obama ally and amnesty’s staunchest proponent.”

Said Rep. Dana Rohrabacher (R-Calif.), “Those of us who elected Eric expected him to be a lot more aggressive than he is right now.”

Cantor is widely expected to win reelection and has retained good relations with House conservatives, in part because of his ongoing outreach to the caucus.

The crux of Cantor’s credibility within the House GOP has been his willingness to raise money for colleagues, connect them with donors and prod them without antagonizing them.

He monitors the House GOP’s pulse, hosting long dinners where he often brings food. (Cantor, the sole Jewish Republican in Congress, keeps kosher.) He stays in touch with members via frequent text messages and phone calls over the course of a single day.

But Cantor and his aides, cognizant of the need to keep conservatives in their camp, have gone to great lengths to balance Cantor’s stew of platitudes with chunks of conservative red meat.

Earlier this month, Cantor released an updated report on Obama’s “imperial presidency” and brought the Enforce the Law Act, which chastised the president for his administrative actions, to a vote.

His challenge is to find the right balance.

To voters, he must present the GOP as a family-friendly enterprise, driven to solve problems rather than advance a conservative wish list. Months after a government shutdown divided Republicans and caused their poll support to sink, Cantor has prioritized appealing to middle-class Americans, especially those who may have been alarmed by the fiscal drama.

Success for Cantor would mean expanding the GOP’s 233-seat House majority while cementing his stature as a national force in the party.

“It is an important moment for him,” said Republican Vin Weber, a former Minnesota congressman who advised Newt Gingrich before the Georgian became House speaker in 1995. “The party is trying to figure out how to move from being an opposition party to an alternative party, and people are looking to Eric to bridge the gap.”

Longtime House GOP members said Cantor, who they said would easily be elected speaker should Boehner step down and House Republicans retain their majority, is behaving in a predictable way for someone hoping to remain a conservative leader while ensuring that the party does not lurch too far to the right and lose seats.

“He certainly has refined his style,” said Rep. Frank D. Lucas (R-Okla.), chairman of the Agriculture Committee.

A glance at Cantor’s Web site captures his new approach.

At the top, spread across the entire page, is a picture of Cantor speaking with children at a school cafeteria. Elsewhere, Cantor is seen chatting with Obama and Vice President Biden, and there is a post about a trip he took this month to Mississippi, where he participated in the annual Congressional Civil Rights Pilgrimage and honored Lewis, a movement icon.

Some Democrats have dismissed Cantor’s undertaking as little more than political posturing designed to make an overwhelmingly conservative House GOP caucus seem more middle of the road.

“Cantor and his staff are very good at putting together small-bore, feel-good items,” said James P. Manley, a former adviser to Senate Majority Leader Harry M. Reid (D-Nev.). “But he’s hamstrung by his party’s right wing.”

Cantor first laid out his new direction in February, when he issued a 2,000-word memo detailing legislative goals. He labeled the project “An America That Works.” On Friday, he sent GOP members an update, underscoring his commitment to his playbook.

Rather than rallying House conservatives to make more demands of the president, such as their past fruitless attempts to pressure him to defund his health-care law, Cantor has urged his Republican colleagues to rethink their expectations for a divided government. He has told them to engage with Democrats on less controversial fronts, such as reducing home heating costs and modifying flood-insurance regulations.

Earlier this month, in a rare instance of bipartisanship, the Senate passed one of Cantor’s bills, which would move funding formerly allocated to presidential conventions to cancer-research programs at the National Institutes of Health.

As the Senate voted, a cheer went up in Cantor’s second-floor suite at the Capitol. Obama is expected to sign the legislation this month.

Cantor’s latest venture is creating an alternative health-care plan.

Those deliberations accelerated this month after Republican David Jolly’s upset victory in a special House election in Florida in which the campaigns focused on the law. Working alongside House Majority Whip Kevin McCarthy (Calif.), Cantor has pledged to bring a refreshed Republican plan to the floor this year. Cantor said it would blend previous conservative proposals, such as a bill offered last year by Rep. Tom Price (Ga.), who is one of the conservative bloc’s leading figures.

Even on health care, Cantor is treading carefully, making sure conservatives are on board with the plan before it is introduced. Every week, he checks in with McCarthy about emerging concerns. Conservatives’ unease about bringing a comprehensive, single GOP bill to the floor has led Cantor to avoid setting a deadline for a final package.

Republicans have come up with an outline of their health-care plan, he said. Agreed-upon elements include an expansion of state-based high-risk insurance pools and the promotion of health savings accounts.

Cantor is receiving help from an outside advocacy group formed by some of his former staffers, including John Murray, his former deputy chief of staff, and Stacey Johnson, his former political director. The YG Network is an organization that says it supports “conservative center-right policies.”

The group held a policy summit over the weekend for self-

described “reform conservatives.” The event featured, among others, a presentation from the Ethics and Public Policy Center’s Yuval Levin, who has become an influential shaper of House Republican policymaking by advising leaders to make a case revolved around supporting civil society and families rather than focusing on budget reductions.