Outside Congress, Democrats and labor unions are fighting for an increase in the federal minimum wage. But inside the Dome, Democrats are strapped for political capital to pass legislation as they engage in a multifront battle against Republicans to extend jobless benefits and protect social programs cut by the sequester.

Even approving unemployment benefits before the end of 2013 is shaping up to be a tough haul for Democrats, who so far have failed to negotiate an extension as part of year-end budget talks. And though senators such as Tom Harkin of Iowa have proposed minimum wage legislation, it’s unclear whether there’s any room to attach such a proposal to pending must-pass bills such as the defense authorization. And there certainly is not a strong desire from the GOP-controlled House to pass a stand-alone bill.

But as Republicans try to avoid discussing the issue of pay minimums, Democrats are increasingly turning to it, boosted by a shift in the White House’s economic talking points and current labor unrest nationwide. On Wednesday, President Barack Obama made boosting minimum pay for American workers one of the cornerstones of a major economic address on income inequality. On Thursday, fast-food workers in 100 cities engaged in a strike over wages, including federal contract workers just a stone’s throw from the Capitol at a McDonald’s in the Smithsonian’s National Air and Space Museum.

“A broad majority of Americans agree we should raise the minimum wage. That’s why, last month, voters in New Jersey decided to become the 20th state to raise theirs even higher,” Obama said in his speech in Washington. “I agree with those voters, and I’m going to keep pushing until we get a higher minimum wage for hard-working Americans across the entire country. It will be good for our economy. It will be good for our families.”

Though Obama highlighted what he believes to be the moral urgency of increasing minimum wage, the overwhelming focus on the Hill has been on how to extend unemployment insurance.

House Democrats held a steering committee hearing Thursday on the economic impacts of canceling federal jobless benefits. The administration has estimated that 1.3 million Americans would be immediately affected by a lapse in benefits if Congress fails to act by the Dec. 28 deadline, with an additional 3.6 million people potentially affected by the end of 2014.

The problem is that there are very few must-pass vehicles remaining this year to carry any provision, let alone social welfare programs that Republicans largely oppose.

Senate Budget Chairwoman Patty Murray, D-Wash., and House Budget Chairman Paul D. Ryan, R-Wis., are not planning to include an extension of jobless benefits as part of their larger budget conference framework. Democrats potentially will need another way, whether by bundling with expiring tax extenders or doctors payments, to approve those benefits.

“This is on top of the resistance to raising the minimum wage, for cutting $40 billion out of food stamps,” House Minority Leader Nancy Pelosi, D-Calif., said at the hearing on unemployment insurance benefits Thursday. “I mean, how unconscionable can that be? Pell Grants, now wanting to cut Pell Grants, which are providing education for low-income families. … The list goes on and on of the compounding of all of these things that are not really a budget that is a statement of our values.”

Congressional Democrats are now facing the uncomfortable political reality — largely as a result of the budget agreements they have made over the past few years — that they will have to choose which benefits to the poor they prioritize. And that could leave them unable to pass the minimum wage increase Obama is now touting.

An aide to Senate Majority Leader Harry Reid said the Nevada Democrat is interested in bringing a minimum wage bill to the floor. And an aide to Harkin, whose bill would raise the federal minimum wage to $10.10 per hour, said the senator is working with Reid to schedule a vote “as soon as possible.”

Progressives are so skeptical that Congress will be able to act on the minimum wage that members of the House Progressive Caucus are urging Obama to work unilaterally without them.

In a letter to the president first reported by National Journal, Reps. Raúl M. Grijalva of Arizona and Keith Ellison of Minnesota said they believe Obama can and should increase the minimum wage by executive order.

Republicans have said they believe that a federal increase in the minimum wage is unnecessary because certain states have their own laws mandating higher pay and that such a move would unduly burden employers with higher overhead costs.