The marijuana petition has more than 55,000 signatures, 20,000 more than any other issue on the site, Roll Call reported Monday.
A petition needs 25,000 signatures to trigger an official response.
"The political mind is pretty simple: What can you do for me, what can you do to harm me," said Allen St. Pierre, head of the National Organization for the Reform of Marijuana Laws, which began the White House petition. "We're not effectively casting that in either direction."
St. Pierre told Roll Call online petitions help to engage supporters who can call and write Congress as well as spread the word.
His group's political action committee distributed about $10,000 in the previous election. Another group, the Marijuana Policy Project, spent nearly $80,000 in the 2010 election and $60,000 for lobbying last year.
"We are not nearly as organized to put together the type of donations and [political action committees] that arrest and immediately catch the attention of the elite body politic," St. Pierre said.
While the bill is unlikely to pass, Marijuana Policy Project spokesman Morgan Fox said it is a "placeholder" to "keep the conversation alive."
Marijuana advocates said polls indicate most Americans, especially younger people, support their argument, Roll Call reported. There is opposition from groups such as Mothers Against Drunk Driving and Drug Free America Foundation.
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