Forget the “fiscal cliff”: When it comes to the nation’s most pressing concerns, other matters trump financial calamity.

Several thousand Americans, for example, are calling on President Obama to nationalize the troubled Twinkies industry to prevent the loss of the snack cake’s “sweet creamy center.”

Thousands more have signed petitions calling on the White House to replace the courts with a single Hall of Justice, remove Jerry Jones as owner of the Dallas Cowboys, give federal workers a holiday on Christmas Eve, allow members of the military to put their hands in their pockets and begin construction of a “Star Wars”-style Death Star by 2016.

And that’s just within the past month.

The people have spoken, but it might not be what the Obama administration expected to hear. More than a year after it was launched, an ambitious White House online petition program aimed at encouraging civic participation has become cluttered with thousands of demands that are often little more than extended Internet jokes. Interest has escalated in the wake of Obama’s reelection, which spurred more than a dozen efforts from tens of thousands of petitioners seeking permission for their states to secede from the union.

The idea, dubbed “We the People” and modeled loosely on a British government program, was meant to encourage people to exercise their First Amendment rights by collecting enough electronic signatures to meet a threshold that would guarantee an official administration response. (The level was initially set at 5,000 signatures, but that was quickly raised to 25,000 after the public responded a little too enthusiastically.)

Administration officials have spent federal time and tax dollars answering petitioner demands that the government recognize extraterrestrial life, allow online poker, legalize marijuana, remove “under God” from the Pledge of Allegiance and ban Rush Limbaugh from Armed Forces Network radio.

The last issue merited a formal response from the Defense Department: “AFN does not censor content, and we believe it is important that service members have access to a variety of viewpoints,” spokesman Bryan G. Whitman wrote to the more than 29,000 people who signed the anti-Limbaugh petition.

The “We the People” program emerged in the news last week when petitioners demanded that Obama block an appearance at Sunday’s “Christmas in Washington” concert by Psy, the South Korean “Gangnam Style” singer who is under fire for anti-American lyrics. The program’s rules require that petitions relate to “current or potential actions or policies of the federal government,” prompting the White House to pull down the petition because Obama has no authority over booking at the privately run charitable event.

As quirky — and potentially embarrassing — as some of the most popular petitions are, White House officials profess to be encouraged by public interest and participation. More than 94,000 petitions have been created, and they have garnered 5.9 million signatures from 4 million users, said Macon Phillips, the White House director of digital strategy. The administration has issued 82 responses.

“We could create a carefully staged social-media experience . . . but it would be the most boring thing imaginable,” said Phillips, who oversees a staff of 11, including three who work extensively on the project. “Would I prefer not to go around the office here and be known as the guy carrying [obscure] petitions? That would be nice. But I view this overall as a huge win because we are able to address issues people care about on a scale that’s never happened before.”

Unlike some of his peers, Phillips, 34, who worked on Obama’s first campaign, believes there’s no such thing as bad publicity. He contends that the notoriety surrounding the more offbeat petitions has helped drive interest to more serious efforts, including some that have had a direct effect on policy.

As an example, Phillips points to the administration’s response to two petitions that garnered more than 100,000 signatures opposing legislation aimed at forcing Web sites to monitor users for copyright infringements. In an 820-word response, the White House indicated it would not support the bills as written — and both were later dropped by Congress.

“I don’t think the administration would have weighed in as quickly” without the petitions, said Phillips, who envisions linking “We the People” to Facebook and other social media to solicit even greater participation.

On a less serious topic, the White House agreed to release its homemade Honey Brown Ale recipe to the public in September after more than 12,000 people signed an electronic petition.

“With public excitement about White House beer fermenting such a buzz, we decided we better hop right to it,” White House assistant chef Sam Kass wrote in a playful response titled “Ale to the Chief.”

Not every request achieves such immediate results.

Stephen Bassett of Bethesda had high hopes when he petitioned the White House last year to disclose knowledge of human contact with extraterrestrial life and acknowledge government efforts to cover it up. His initiative attracted 12,000 signatures.

Bassett is still waiting for E.T. to phone his home. Phil Larson, a policy and communications specialist in the White House Office of Science and Technology Policy, wrote in response that there is “no credible evidence of extraterrestrial presence here on Earth.”

Still, Bassett, executive director of the Paradigm Research Group, which is dedicated to uncovering what it says is suppressed information about UFOs, feels he accomplished his goal of bringing attention to a subject some might consider fringe.

“You always hear people say Social Security is the ‘third rail’ of American politics, that no one is going to touch it,” Bassett said. “But no one considers Social Security a fringe issue. The E.T. issue is the most highly charged third rail there is.”

Phillips acknowledged that during internal deliberations before the program was launched, some administration officials expressed concern that awkward topics would draw attention. But in the end, they agreed that the program would inform the populace and help set the record straight.

Many petitioners complain that, even with the more serious petitions, the administration has issued boilerplate responses with little opportunity for follow-up. One petition asked the White House to take the petitions more seriously; that one garnered 37,000 signatures.

Andrew Rasiej, founder of Personal Democracy Media, which examines the nexus between politics and technology, said it’s not surprising that petitioners holding un­or­tho­dox points of view often dominate the site. “The organized minority is always more effective than the disorganized majority,” he said.

Last month, Rasiej’s organization suggested in an online essay that the administration hold more conference calls with petitioners and find ways to allow them to talk to one another to help bridge partisan and ideological divides.

Those divides are on full display on the site. Seven secession petitions are currently among the top three dozen on the list, including one from Texas with 120,000 signatures. The second most popular — one of many petitions seeking to legalize marijuana — has 65,000.

Requests for a recount of the presidential election results, the repeal of the health-care law and the impeachment of the president each have surpassed the 25,000-signature threshold — even though the recount petition was based on voting statistics that a fact-checking Web site rated “Pants on Fire” false.

There is at least one request focused on the fiscal cliff. A petition posted on Nov. 18 calls on the White House to reach bipartisan compromise on the issue with Congress so young people “can have bright futures.”

Fewer than 650 people have signed it.