Michelle Obama’s altercation with a lesbian activist this week sparked a debate about the merits of heckling. The popular first lady’s many fans loved the way she stood her ground, and an outburst from an irate LGBT activist struck many as surprising given President Obama’s record of support for gay rights.

Yet the episode revealed an important aspect of the Obama presidency – the feeling among many of his own core constituents that the best and only way to score policy victories from the administration is to push, pressure and cajole an often reticent White House into action.

President Obama and Michelle Obama greet people while visiting Section 60 at Arlington National Cemetery on May 27 in Arlington, Va. (Mark Wilson/Getty Images)

And by confronting the first lady on Tuesday night, Ellen Sturtz, a lesbian activist, signaled the start of a renewed push by gay rights activists to turn up the heat on Obama yet again. This time, the goal is a long-sought executive order prohibiting discrimination on the basis of sexual orientation or gender identity by federal contractors.

Gay rights activists repeatedly heckled the president during his first term, pushing the White House to be more aggressive on repealing the military’s Don’t Ask Don’t Tell policy and to reverse its initial decision to stand by the Defense of Marriage Act in court. Obama’s vocal support last year for same-sex marriage rights opened the floodgates for donations by gay donors to his reelection effort and transformed Obama into a gay-rights rock star.

Immigration advocates were so taken by the gay rights movement’s successes that they adopted a mantra — “It’s time to go all LGBT on their ass” — as Hispanic activists and other immigrant advocates began to personally challenge the president to take executive action to halt many deportations. (This essay by Frank Sharry explains the connection.)

Sturtz’s disruption of the first lady’s speech at a D.C. fundraiser drew an unexpected response from Michelle Obama and garnered worldwide attention – but it was hardly spontaneous.

The protest was orchestrated by the militant group GetEQUAL, which organized many of the first-term protests targeting Obama and is vowing more disturbances to come until Obama signs the anti-discrimination order. Sturtz paid $500 for the right to attend the Democratic Party fundraiser that she then overshadowed.

Activists, who believed Obama would sign the order after last year’s election, have grown frustrated that the matter has not been resolved. Their anger has grown exponentially as White House officials decline to say whether such an order is even on the table. Officials now refer to the order as “hypothetical,” even though it is widely believed that administration staffers long ago drafted it and sent proposed language to the White House for consideration.

Activists say they are moving to escalate pressure now on several fronts.

One gay rights group, Freedom to Work, filed a lawsuit last month in Illinois against a prominent federal contractor, Exxon-Mobil, accusing the oil giant of discriminating against LGBT job applicants. Exxon-Mobil executives and shareholders have repeatedly rejected adopting anti-discrimination policies that include sexual orientation and gender identity protections in the company’s official equal employment opportunity documents.

Freedom to Work’s president, Tico Almeida, who met with senior White House aides on the executive order last year, said the Exxon-Mobil suit is designed in part to highlight Obama’s lack of action. The group filed its Illinois suit after submitting fictitious resumes for a job opening — one that identified a candidate as being LGBT and another that appeared to be from a lesser qualified straight applicant. The LGBT applicant received no calls back, while the straight one did, the group says.

"I hope that our proactive efforts to root out discrimination among federal contractors will help the White House realize that the Obama administration needs to get in the game and do more to ensure that qualified LGBT Americans get a fair shot to hold a job no matter who they love,” Almeida said.

On another front, some prominent gay Democratic Party donors say they will withhold any additional giving until Obama signs the order.

“I am too old to sit back and play nice while our friends continue to fail to live up to their rhetoric,” said Jonathan Lewis, a major donor to Democrats and gay rights causes, in an e-mail to The Post. “I will either die equal or go out fighting.”

The move by frustrated donors has sparked a fierce debate on a private listserv, where the Democratic National Committee’s treasurer, Andrew Tobias, has repeatedly weighed in over the past two weeks pleading for patience.

The e-mail exchanges heated up last month when Democratic senators declined to fight for a provision in the immigration bill that would have allowed citizens to bring their same-sex immigrant spouses into the country legally.

“You and all the rest of us are absolutely right to be frustrated by the delays and to keep pushing (I’m hoping this Exxon/Mobil hook might be the one that puts it across the finish line),” Tobias wrote in one e-mail, first reported by the Washington Blade.

Tobias added an argument that, for all the frustrations, the Democrats are generally more sympathetic than Republicans: “Until that changes, those of us who can afford to plant the seed corn for further success in 2014 and 2016 could not possibly make a more leveraged investment in equality.”

White House officials have said Obama favors legislation, such as the proposed Employment Non-Discrimination Act, which officials argue would be more permanent than an executive order. They offered no hint that the episode involving Mrs. Obama changed the White House position on issuing an order.

“As we’ve said before, the White House has no updates regarding a hypothetical executive order on LGBT non-discrimination for federal contractors,” White House spokesman Shin Inouye said in an e-mail.