Here’s how to kill three Republican birds with one stone: (1) leverage the massive federal government contracting system to (2) legislate around an intransigent House majority and (3) benefit about 2 million LGBT people.

That is what President Obama will do Tuesday when he signs an executive order banning all federal contractors—i.e., companies who together employ about 28 million Americans—from firing employees on the basis of sexual orientation.

It may surprise readers to know that, in 29 states, one can be fired simply for being gay—but indeed one can. Federal legislation to make such a termination illegal—as it already is for race, gender, religion, and national origin—has died repeatedly in the Republican-controlled House of Representatives. This year’s version, the Employment Non-Discrimination Act (ENDA), is expected to fail as well, notwithstanding its newly broad exemption for any religiously affiliated organization, including hospitals, schools, nursing homes, and even Mormon-owned malls.

So, as Obama did with the minimum wage a few months ago, he has implemented his own private ENDA. Unlike the minimum wage hike for federal contractors, however, which isn’t likely to affect many people because they already make more than $10 per hour, Tuesday’s executive order not only will protect an estimated 2 million LGBTs from losing their jobs, but also will normalize sexual orientation nondiscrimination among most of America’s largest corporations.

This is a big deal. LGBT activists have generally regarded employment nondiscrimination as the “third leg of the stool”—the other two being same-sex marriage and the end of Don’t Ask, Don’t Tell. But it’s also the thickest of the three. Many more LGBTs have jobs than get married or serve in the military—including some of the most vulnerable. To get a sense of the crisis, check out this incredible spread of “LGBT People Fired in 2013” from the gay newspaper The Advocate.

Perhaps most important, Obama’s executive order is said to include gender identity and gender presentation. Transgender people routinely are fired when they transition, especially if they don’t yet conform to stereotypes of how ladylike ladies and manly men are supposed to look.

And yet the president declined to take this action two years ago, when he was pressured by major LGBT rights organizations. What’s changed? Three things.

First, obviously, public opinion on LGBT people has shifted significantly since April 2012. It is now widely understood that gays are not sexual predators, sexual deviants, or abominations but people who happen to love other dudes or other women. There is much that is distinctively different about LGBT people, but sexual orientation is about as relevant to the ability to assemble rotors or serve meatloaf as eye color or the dislike of country music. Most Americans now know this.

Second, as Obama said in January, he has given up on Congress acting on anything resembling a socially progressive agenda. As promised, he’s now doing it on his own.

And finally, it’s June: pride month, with a Democratic National Committee LGBT fundraiser Tuesday in New York and a White House LGBT reception on June 30. Is it cynical to make such a major announcement the day before a $1,250-per-plate (minimum) dinner that Obama himself is attending? Nah, just politics.

Of course, as an executive order, the act can be erased if Cruz/Paul/Rubio/Bush/Perry takes Ohio in two years. Yet that may be unlikely. Once a company adopts a nondiscrimination policy, revoking it is particularly ornery—especially once the ludicrous fears of drag queens in the secretary pool fail to materialize.

Moreover, 87 percent of Fortune 500 companies already protect gay people, and nearly half protect trans people as well. That’s due in part to the milk of human kindness, in part to extensive work by the Human Rights Campaign, and in part to simple economics: You don’t want to miss out on 5 percent of qualified jobseekers, with higher percentages in major urban centers.

At the same time, while Obama’s order covers more than 10 percent of the American work force, that leaves a whole lot of LGBT workers left over. And in a political climate where rabid right-wingers such as Tony Perkins can torpedo the candidacy of any Republican deemed to have caved to the “gay agenda,” few in the GOP are willing to take the risk. No one wants to be the next Eric Cantor.

One can only hope that our national growing-up about gay people will get to the point where opposing equality is more dangerous than supporting it. Even for Republicans.