One of the summer’s hottest local stories has become the standoff between the D.C. Council and Wal-Mart over how much the big-box behemoth should have to pay its Washington workforce.

The dust-up could end up touching Congress in several ways, beyond the sudden uncertainty about whether Hill staffers will have a new place for lunchtime shopping by the end of the year. (One of the chain’s first stores under construction in the city is at First and H streets Northwest, right behind the Government Printing Office and no more than a 20-minute walk from the Russell Senate Office Building.)

Whether city leaders end up sticking with or backing away from the “living wage” measure approved last week — it would require big retailers to pay starting wages 50 percent above the District’s regular minimum — could help steer the fate of President Barack Obama’s moribund-for-now proposal to raise the federally guaranteed hourly wage floor.

Whether Republicans end up moving legislation to block the local ordinance would indicate how forcefully, if at all, they want to apply the congressional prerogative to trump local rule. Whether Democrats move assertively against such a GOP intrusion would reflect how enthusiastic they are about advancing the agenda of organized labor.

And whether Wal-Mart would even seek such intervention will offer insights into how the lobbying team for the world’s largest retailer plans to prioritize its interests at the Capitol.

D.C. Mayor Vincent Gray has until the end of this week to sign or veto the measure. (The city’s regular minimum wage of $8.25, or $1 more than the federal floor, would go up to $12.50.)  The company doesn’t yet have any stores open in the city, but the one on H Street is among three nearing completion, and plans are well along for three more in neighborhoods clamoring for more connection to Washington’s vaunted economic renaissance.

Wal-Mart is vowing that, if the higher wage law takes effect, it will abandon preparations for that second group of developments immediately while pondering its legal and financial options for pulling out of the others.

If Gray vetoes the measure, he would be echoing a move in 2006 by the Democratic mayor of another pro-labor city, Richard M. Daley, whose rejection of a living wage for big-box retailers sped along the opening of eight Wal-Marts in Chicago.

It would also probably be the end of the matter, because nine council votes are needed to override a council decision, which in this case passed 8-5.

But if the mayor calls the company’s bluff and signs the bill, it would indicate confidence that, with organized labor’s backing, he could get away with it — maybe with Wal-Mart but, if not, probably with the city’s voters and very likely with Congress.

For a mayor who’s put some visible effort into smoothing the city’s notoriously rocky congressional relations, embracing the living wage concept would be a bold change of course: He would be making D.C. a showcase for progressive values just as Republicans in the House are contemplating more efforts at making the city an unwitting display case for conservative social values.

Congress has the power to permanently negate enactment of any District statute. But it has to do so through the regular legislative process, which means it hardly ever happens. It’s especially unlikely given the Capitol’s partisan split.

Instead, whenever it has been in the House majority, the GOP has taken to writing language dictating some sort of conservative social policy (or preventing the city from pursuing its more liberal policies) into the annual spending bill providing the federal payment to Washington in lieu of taxes.

This year’s version is being considered by House Appropriations this week. It’s already going to include language chiding D.C. voters for approving a budgetary autonomy referendum this spring — though not actually reversing the outcome. There are rumblings that some Republicans are working on an amendment that would block the city, at least for the coming year, from putting a two-tier wage floor into effect.

Such language would presumably draw concerted and public protest from top Democrats, for a couple of reasons.

They are eager for any platform to promote their commitment to bolstering stagnant wages for the working class, which they expect to place among their top promises in their economic platform for the 2014 midterm. And they have lamented that Obama — although he did talk it up in his recent meeting with the Congressional Black Caucus — hasn’t done more to promote his State of the Union call for raising the minimum wage to $9 and then mandating yearly cost-of-living adjustments.

But putting their agenda for working people back in the public eye is mostly a strategy for next year, which leaves Democrats to do only what they can this year to make organized labor happy. The main pillar in the strategy has now become clear: getting Obama’s three nominees for the National Labor Relations Board confirmed, even if it takes the “nuclear option” of forcing limits on filibuster to get the job done.

Making sure a $26,000 annual salary, instead of $17,160, goes to just 1,800 minimum-wage workers — none of whom has even been chosen to pin the yellow smiley faces to their uniforms — should be relatively easy compared to remaking the culture of the Senate.