For more than two years, President Obama has endorsed reducing Social Security payments as part of an ambitious deal to tame the national debt. But then Sen. Elizabeth Warren (D-Mass.) — viewed by supporters on the left as a potential 2016 presidential candidate — embraced a far different proposal: increasing benefits for seniors.

As Obama struggles to achieve his second-term domestic agenda, a more liberal and populist voice is emerging within a Democratic Party already looking ahead to the next presidential election. The push from the left represents both a critique of Obama’s tenure and a clear challenge to Hillary Rodham Clinton, the party’s presumptive presidential front-runner, who carries a more centrist banner.

The left’s influence will be on display in coming weeks when a high-profile congressional committee formed after the government shutdown faces a deadline to forge a budget agreement. Under strong pressure from liberals, the panel has effectively abandoned discussion of a “grand bargain” agreement partly because it probably would involve cuts to Social Security.

“The absolute last thing we should do in 2013 — at the very moment that Social Security has become the principal lifeline for millions of our seniors — is allow the program to begin to be dismantled inch by inch,” Warren said recently on the Senate floor, announcing her support for a bill that would expand the program.

Liberals say Social Security is one example of how Democrats are likely to face sustained pressure in coming months to move in a more populist direction on a host of issues.

She's been in the Senate for less than a year, but Massachusetts Democrat Elizabeth Warren's grasp extends beyond Capitol Hill - thanks to her YouTube presence. (The Washington Post)

“The first Obama administration was focused too much on saving the banks and Wall Street,” said Sen. Tom Harkin (D-Iowa), a liberal who is retiring after four decades in Congress. “There’s going to be a big populist push on whoever’s running for office to espouse these kinds of progressive policies.”

Senate Democrats’ recent decision to abandon the filibuster for almost all nominees was a major victory for liberals, who had long championed the change, and paves the way for left-leaning nominees to join courts and helm agencies.

In addition, liberals have accelerated their push for a higher minimum wage — successfully persuading Obama to support a $10.10-an-hour proposal after he suggested $9 an hour this year. They also are making a case for tougher financial regulations, specifically targeting massive banks they would like to break up.

More broadly, liberals argue that the nation must do more to narrow economic inequality, to expand the safety net to help those who have lost jobs to globalization and to relieve some of the burden of student debt — goals that the president generally shares.

Obama’s defenders say he has a wide array of proposals to help the middle class that have been stymied by Republicans in Congress. Even his willingness to trim Social Security payments — by adopting a stricter formula for calculating benefits — includes protections for the poor, they note.

“It’s real things in the economy that Democrats have been too timid to address or Republicans have blocked them from addressing,” said longtime liberal activist Roger Hickey, co-director of Campaign for America’s Future.

But the push from the left carries political risks for Democrats, who could be accused of being reckless about the national debt or insensitive to the demands of business and economic growth. What’s more, many Americans are uncomfortable with the notion of the government redistributing income far beyond what happens today in order to accomplish basic elements of the populist agenda. Liberal congressional or presidential candidates could pressure more moderate candidates to veer to the left, perhaps reducing their electability.

The arena where the populist push is likely to play out most clearly is in the nascent 2016 presidential campaign. Warren is the object of admiration among liberals, drawing huge audiences for her speeches. She has said she doesn’t plan to run for president, but she hasn’t made a firm commitment to stay out of the race. A spokeswoman said she was unavailable to comment.

At the same time, many on the left view Clinton suspiciously, arguing that longtime advisers to her and her husband, former president Bill Clinton, are too close to Wall Street.

Many liberals also argue that it was these same Clinton advisers — disciples of former Treasury secretary Robert Rubin — who led Obama away from a more populist agenda, embracing conservative thinking on the virtue of spending reductions and entitlement cuts.

“I personally have Clinton fatigue, noting that it was a Clinton team that has been running Obama’s economics,” said Lawrence Mishel, president of the labor-backed Economic Policy Institute. “A Clinton administration seems like a continuation of the same team.”

Some consider the debate an opportunity for Hillary Clinton to embrace a more populist message. Bill de Blasio (D), her New York campaign manager in 2000, was just elected mayor of New York on an inequality agenda.

Top officials at the Center for American Progress — sometimes viewed as a Clinton shadow cabinet — started an independent think tank several weeks ago, the Center for Equitable Growth, to study income inequality. At its Washington opening, Chairman John D. Podesta, who was Bill Clinton’s White House chief of staff, hinted about restoring the domestic success of the 1990s.

“All the gains, I think, to fight poverty and reduce the poverty level during the Clinton administration in which I served have been washed away,” he said.

In an interview, Podesta said the think tank is an academic effort not intended to benefit any candidate in particular. But he said he has no doubt that Hillary Clinton would be able to succeed on populist political terrain.

“I’m an admirer of Senator Warren’s, but I think that Hillary Clinton really connects with working people and she showed that in the 2008 race against Obama,” he said.

Liberals, however, are fawning over Warren, who was the brains behind the new Consumer Financial Protection Bureau and focused on the economic condition of the working class when she was a professor at Harvard. In addition to calling for breaking up the big banks and expanding Social Security, she has proposed a range of new policies to cut student debt.

Warren received a resounding response when she spoke at the AFL-CIO convention this past fall in what many considered an encapsulation of her populist message going forward.

“We know even though pundits and big corporate lobbyists in Washington might need to be dragged kicking and screaming, we know America agrees with us. We believe Wall Street needs stronger rules and tougher enforcement. And you know what? So do more than 80 percent of people,” she said. “Wall Street will fight us, but the American people are on our side.”

Another potential source of pressure building on the left is Sen. Bernard Sanders (Vt.), an independent who caucuses with Democrats. He has said he might run for president if no liberal he considers adequate steps up.

Although his chances would be slim at best, he could serve as an agitator who pulled other candidates to the left — or as a potential spoiler if his campaign got off the ground.

“I don’t wake up every morning saying, ‘Oh my goodness, I really want to be president,’ ” Sanders, who calls himself a democratic socialist, said in an interview. “But somebody’s got to be out there, and if nobody is, I’ll do it.”