It could be dubbed the federal contractor trifecta.  

Employees at businesses that do a lot of work for the government began this election year hoping to benefit in three distinct ways from President Barack Obama’s vow to act on his own whenever Congress deadlocked on his legislative priorities.  

Two of those expectations have now been met. In January he ordered contractors to start paying their blue-collar laborers at least $10.10 an hour, realizing his proposal to raise the $7.25 federal minimum wage to that amount was doomed . And this month he declared that workers on federal contracts must be free to discuss their salaries, so women may more easily expose pay inequities at those companies while legislation that could close the wage gender gap nationwide languishes.  

Now, the pressure will only intensify for Obama to make good in the third area. Lesbian, gay, bisexual and transgender employees being paid under federal contracts want to benefit from the same sort of executive order that is aiding female and low-wage workers. And their advocacy groups, along with allies on the Hill, are signaling they’re tired of waiting for the president to apply his “we can’t wait” mantra to their cause.  

The issue is job bias against LGBT people. While steady advances continue in the states for same-sex marriage — still the paramount political cause of the gay community — outlawing employment discrimination has become the principal gay rights cause in Washington, in part because it’s unambiguously subject to federal regulation or legislation in a way that marriage equality is not.  

Only 21 states have made it illegal to fire or harass someone based on sexual orientation, or to deny a raise or refuse to hire on that same basis. More than 11 million people work in the remaining 29 states for companies without policies protecting workplace civil rights for gay people, according to a recent study by UCLA Law School.  

Last November, 10 Republicans joined 54 Democrats in the Senate to pass legislation that would prohibit gay job bias nationwide at businesses with more than 15 workers, with some exceptions for religious organizations. But House Republicans have no interest in putting the bill on the floor. (Known as the Employment Non-Discrimination Act, or ENDA, it’s currently 16 votes shy of guaranteed passage, in any event.)  

In short, the gay rights community sees their “ask” as a clear parallel to the minimum wage and pay parity issues. They argue Congress isn’t ready to change the situation nationally, so Obama should at least start paving the way by helping out people working for or seeking employment from government contractors. The Labor and Justice departments reportedly signaled support for an executive order to that effect almost two years ago, but the White House concluded that during his re-election campaign was the wrong time for the president to act. And last year, the administration decided to stand aside while solid bipartisan Senate support for ENDA was building.  

But since the Senate passed its legislation, momentum for the companion measure in the House has stalled.  

The bill is co-sponsored by 193 House Democrats, and the remaining half dozen are not likely to add their names. They’re all from culturally conservatives districts and three are in the middle of competitive campaigns: John Barrow of Georgia, Pete Gallego of Texas and Nick J. Rahall II of West Virginia.  

Only two Republicans have signed-on to the bill this year, for a total of eight GOP names on the legislation. Mike Coffman of the Denver suburbs and Michael G. Grimm of New York’s Staten Island are both looking at intense fights for re-election in socially liberal swing districts that Obama carried in 2012.  

But since there are only a handful of Republicans, at most, who might support the legislation, it’s essentially impossible to construct a plausible whip count that would lead to passage. Besides, Speaker John A. Boehner has labeled the bill “frivolous” and said he has no interest in scheduling a debate.  

Which is why the drumbeat for Obama to act has started sounding louder.  

Before the congressional spring recess, 168 House Democrats and 52 Senate Democrats (but no Republicans) sent the president a letter urging him to make abiding by ENDA’s precepts a condition of winning future federal contracts — something Obama signaled he would do as long ago as the 2008 campaign.  

The White House has so far resisted the call. Asked about the matter after the letter arrived, spokesman Jay Carney said the president was still holding out for Congress to clear the broader bill, which he said would make the executive order “redundant.”  

The same might also be said of the minimum wage and pay gender gap directives; those “half a loaf” presidential actions would mostly be supplanted by more sweeping legislation. But it’s also true that an executive order could be written to provide stronger protection for employees on federal contracts than for the rest of the LGBT workforce.  

The root of Obama’s reticence potentially lies elsewhere. He may be calculating he’s reached the political, if not legal, limit on how much he can accomplish on his own authority. Republicans in Congress are already plenty furious at Obama for what they call his “imperial presidency” assertions of power. Another move, especially one that would stoke the culture wars six months before Election Day, could be one step over the line. House GOP leaders have made clear that, for Obama to have any chance of adding immigration to his roster of legislative achievements, he’ll have to secure a big measure of trust.  

Tucking his executive order forms away in a drawer at this point could be an essential first step.