Of the pressing policy questions facing the White House this week — Syria, the National Security Agency, Egypt — it was another that administration officials feared would create the biggest buzz.

“Given the reported medical benefits of marijuana, does the president believe the government should reconsider?” a CNN correspondent asked about the federally banned substance during the White House briefing Wednesday.

No, spokesman Josh Earnest answered, President Obama isn’t high on such a change “at this point.” With a chuckle, he added: “I have the sneaking suspicion that this is going to draw me all kinds of traffic on Twitter.”

The issue may seem superfluous, but consider this: Since Obama took office in 2009, questions about whether he would support legalizing marijuana — for medical or recreational use — have been among the most popular among the public. He has been asked at town-hall meetings, in online petitions on the White House’s Web site, and in an interview with ABC News’s Barbara Walters in December.

“It would not make sense for us to see a top priority as going after recreational users in states that have determined that it’s legal,” Obama told Walters a month after voters in Colorado and Washington supported initiatives to legalize marijuana, even though it remains illegal under federal statutes.

Dan Riffle, the federal lobbyist for the Marijuana Policy Project, talks legalizing pot, libertarianism and stereotypes of a marijuana lobbyist. (The Washington Post)

When the White House created an online petition program called “We the People” in 2011, marijuana-related petitions were so popular that the administration issued four separate responses to 13 petitions with hundreds of thousands of total signatories.

But for all the public pressure, legalization advocates said the president has disappointed them. Though candidate Obama spoke convincingly about his open-mindedness on the issue in 2008, they said, President Obama has largely failed to rein in a Justice Department accused of running roughshod over state-approved medical marijuana clinics during the administration of President George W. Bush.

Under Obama, the advocates said, federal enforcement has increased. In a June study, Americans for Safe Access asserted that the Drug Enforcement Administration raided 270 medical marijuana clinics in 4 ½ years, compared with 260 during Bush’s eight years. The report also concluded that the Obama administration has spent nearly $300 million on enforcement, $100 million more than the Bush administration.

Advocates acknowledge that the number of state-approved marijuana clinics has multiplied rapidly in recent years. But they are pressing for a stronger endorsement of the state laws from the White House than a 2011 memo from Deputy Attorney General James M. Cole that says that federal agents are focused on large-scale traffickers.

“It sounds nice for it not to be a priority for us to go after individual marijuana users, but that statement is virtually meaningless,” said Tom Angell, founder of Marijuana Majority. “The real question is whether the president wants to allow voter-approved systems in these states or whether he wants to intervene and force users to continue buying marijuana on the black market from violent gangs.”

The Justice Department has been mum in the nine months since the ballot initiatives were ratified in Colorado and Washington. Attorney General Eric H. Holder Jr. has promised a position paper, but officials said the review isn’t finished. Colorado is preparing to open recreational marijuana shops in January, and Washington plans to do so in March. Meantime, federal raids on medical marijuana clinics there have continued.

Advocates were encouraged that Obama openly admitted his personal history of smoking pot as a teenager in his 1995 memoir “Dreams From My Father.” Author David Maraniss reported in his book “Barack Obama: The Story” that high school friends considered Obama an enthusiastic leader of a group called the “Choom Gang,” slang for marijuana smoking.

But Obama’s tone changed soon after he was sworn in. In March 2009, amid the global financial crisis, the White House solicited questions online for a town hall-style meeting and was overwhelmed by contributors suggesting that legalizing pot would boost the economy.

During the forum, Obama interrupted the moderator to address the “most burning” question, as one YouTube video called it.

“I don’t know what this says about the online audience,” Obama quipped, drawing laughs, “but this was a fairly popular question and we want to make sure it was answered. The answer is no, I don’t think that is a good strategy to grow our economy.”

Christian Sederberg, an attorney who helped lead the push in Colorado, said public officials play down the seriousness of the debate by joking about stoners. After voters legalized pot, Colorado Gov. John Hickenlooper (D) “came out and said don’t break out the Cheetos and Goldfish just yet,” Sederberg said.

At a fundraiser in San Francisco in June, Vice President Biden related an anecdote about Mexican leaders who pushed back against U.S. concerns about border violence by accusing Americans of fueling the demand for illicit drugs.

“You can make my job a lot easier if you would stop smoking so much pot,” Biden joked to the donors, according to one person at the event.

This month, Holder gave legalization advocates hope when he announced that low-level, nonviolent drug offenders with no ties to gangs or large-scale drug organizations will no longer face severe mandatory sentences. And CNN’s medical analyst, Sanjay Gupta, once considered by Obama to become surgeon general, produced a report this week about why he endorses marijuana for medical use.

Gupta’s about-face is what prompted the question during Wednesday’s briefing. As Earnest spoke, Twitter lit up with reaction, mostly pot gags and mostly from reporters. (“Choom Gang to roll out plan,” one scribe quipped.)

Hesitant to get into the weeds on pot policy, Earnest promised to follow up later.

“Maybe I’ll bring you some Doritos later,” the reporter replied.

Juliet Eilperin contributed to this report.