President Obama says he’s going to focus for the rest of his tenure on what he calls “the defining challenge of our time”—a cluster of issues including income inequality, stalled upward mobility, long-term unemployment, and wage stagnation. It’s an admirable pledge and, 50 years after Lyndon Johnson urged Congress to declare war on poverty and unemployment, a timely one. But even if his attention doesn’t wander, the odds of Obama having significant impact are long. In contrast to other issues, like the environment and even gun control, presidents armed with nothing but executive powers can’t do much to affect the economy. They need Congress to act—and how often does that happen these days?

The cupboard isn’t entirely bare as Obama looks for ways to increase jobs and decrease inequality on his own. But no one should mistake a marginal nudge with a substantial achievement. Consider that in September 2011, in his American Jobs Act, Obama proposed spending $50 billion on job-generating infrastructure projects, and creating a National Infrastructure Bank capitalized with $10 billion. The plan went nowhere thanks to Senate Republicans who blocked it, and Obama eventually fell back on executive action on a much smaller scale—speeding up the federal review and permit process for major infrastructure projects. But he’s still hoping for real money and went on the road last summer to beg Congress to step up.

Immigration reform, another Obama priority, is also a prospective economic boon. The non-partisan Congressional Budget Office has found that the sweeping bill passed by the Senate last year and languishing in the House would reduce the deficit, grow the economy and bolster Social Security. “Immigration is as close a thing to a win-win-win as we have in public policy these days,” says Jason Furman, chairman of the White House Council of Economic Advisers.

In the absence of congressional action, Obama has made do with his June 2012 policy of deferring deportation of many undocumented youths brought to America by their parents when they were children—“young people who want to staff our labs, or start new businesses, or defend our country,” as he put it. That is minimal compared with what Congress could accomplish by turning millions of illegal immigrants into citizens or legal residents who earn degrees, get drivers’ licenses, pay taxes, and have unfettered access to the American Dream. Still “expanding opportunity is a way of reducing inequality,” even if it applies to relatively few people, says Bruce Reed, who was domestic policy director in the Clinton administration and was until last month chief of staff to vice president Joe Biden.

Reed also points to unilateral moves by Obama to make colleges more transparent and accountable for their results, tie school reforms to federal aid, and expand access to broadband in rural areas and poor communities. Back in the 1990s, he recalls, Bill Clinton created a literacy initiative and a welfare-to-work partnership that helped thousands of businesses put hundreds of thousands of people to work. “You can’t raise wages by executive order. You can’t change the tax code by executive order,” Reed told me. “But it is possible to look at every aspect of federal policy that might be upside down and explore what can be done with the stroke of a pen to set it straight.”

Republicans and unions point to a narrow way Obama could grow jobs: by approving the Keystone XL Pipeline that would carry oil extracted from tar sands in Alberta to the Gulf Coast. The State Department has estimated the project would create the full-time equivalent of a few thousand specialized construction jobs, a few dozen permanent jobs, and a ripple effect of about 42,000 jobs, which .02 percent of U.S. employment, a figure that Obama is weighing against environmental considerations. His decision is expected early this year.

Ari Fleischer, who was George W. Bush’s press secretary, talks about the high poverty rate of households headed by single women. Obama, he says, could “put a real focus on marriage and on the benefits of marriage and how men have an obligation to stay in relationships and raise children,” by using his bully pulpit. “Sometimes it takes a president to make breakthroughs take place,” he told me.

White House aides talk about the bully pulpit, too, but they envision Obama using it to press businesses to hire the long-term unemployed. Their other ideas for executive action include connecting businesses and community colleges to coordinate college programs with what companies need, and continuing to review regulations to see which can be streamlined, simplified and made more flexible. They don’t mention Keystone. They do mention Congress.

“The biggest impact you can have on the macroeconomy requires legislation,” Furman said recently at a Third Way breakfast. He offered the examples of immigration, infrastructure, universal pre-kindergarten, business tax reform, raising the minimum wage and renewing emergency unemployment benefits for the long-term jobless, and said there was no way Obama would spend the rest of his presidency trying to make the Obamacare website “better and better and better and better until it’s just the best thing in the history of humanity. There’s a lot of other things we want to do.”

The inevitable question is how to get them done, given the recalcitrance of congressional Republicans and the infinite complications of the legislative process. Furman was undeterred. Bush signed a minimum wage increase and Clinton signed one passed by Newt Gingrich’s Republican House, he said, and “there’s no reason that we shouldn’t be able to do something like that.” He pointed to Republicans who want to “do something bigger, something longer-lasting” on infrastructure investment as part of a highway bill due in September; business leaders and GOP economists believe preschool is an important ingredient for U.S. economic growth. Many things are possible based on past precedents, hard deadlines and bipartisan support, he maintained, and all of it matters “for inequality and the economy more broadly.”

Recent history makes Furman sound like a cockeyed optimist, especially given the real prospect of a Democratic drubbing at the polls in November. But Obama and his team can’t afford to go into the next three years with a defeatist attitude. Republicans, meanwhile, may eventually decide they need a few accomplishments to campaign on this fall. It looks like House Speaker John Boehner already has come to that conclusion, given that he recently hired an immigration-reform specialist with bipartisan credentials. Combine that with an emerging consensus among Hispanics and some pundits that legal residency is more important than a path to citizenship, and immigration reform—though not the most obvious of income-related issues—could be the most significant economic advance of 2014.