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In the final 11 months of 2013, just 20 petitions earned enough signatures to get responses and half remained unanswered as of the new year.

Still, plenty of backers say the project has great potential and praise the White House for its willingness to try to work through the problems.

Nicco Mele, who studies social media as an adjunct lecturer at the Joan Shorenstein Center on the Press, Politics and Public Policy, said the White House deserves credit for sticking with the system. He said he groaned early on when the White House opened itself to questions, which were dominated by inquiries about marijuana legalization.

“I thought, ‘Oh God, there it goes. They’re never going to try anything like this again,’” he said.

Instead, the White House has kept working to try to strike a balance and is sticking with the petition program even though the payoff is not clear.

“I think that’s great,” Mr. Mele said. “I think that’s evidence they’re trying to figure out how to build a tool that’s responsive, that’s useful. I pretty unequivocally give them a lot of credit for it.”

Matt Loff, co-founder of Visionist Inc., who has looked at the locations of people signing the petitions, said they have been strikingly bipartisan. He took part in the White House’s “hackathon” last year, which gave programmers and tech specialists a chance to manipulate data on the We the People site. Mr. Loff built a tool to track the political leanings of people who sign the petitions by tracking their ZIP codes.

“I ended up a little less cynical than when I started,” he said. “Initially, I figured there are obviously a lot of polarizing issues brought up on the petition site. My expectation was every issue would have a clear slant to it, people who signed petitions would be all from red states or blue states depending on topic. What I found is of the issues with responses outside one particular region, most had a balance between the two.”

The White House has said the goal isn’t to change its policies, but to give people a chance to organize around common interests.

Mr. Snider said the White House should be more forthcoming about sharing information if that is the case. Right now, it gives out only the initials and locations of petition signers. Mr. Snider said petition organizers should get email addresses as well.

“You’ve got 30 days to get through this incredible hurdle and you don’t get the benefit — the White House gets the benefit, not you,” he said.

Mr. Snider said he would lower the threshold it takes to earn a response and try to make the responses more — well, responsive.

“It’s nice that they promise a response, but they’re not going to say anything controversial for the most part,” he said.

The White House has taken a firm line in some of its responses. Replying to a petition alleging voter fraud in Mr. Obama’s 2012 election victory and in one Ohio county in particular, the White House disputed the petition’s numbers and pleaded for common ground.

“You don’t have to support President Obama or his vision for this country. But you have to acknowledge that all Americans, even those with whom you disagree, have the right to help to set our nation’s course,” the White House said. “That’s a truth that unites us all as citizens, and it sets up a basic agreement — one that makes us an example for other nations, which justifies our democratic experiment: the understanding that the elections we lose are still legitimate.”

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