"Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.
-The First Amendment, United States Constitution
The whitehouse has opened up the "We the People" section of the website so that anyone can create a petition and get people to sign it. If 5000 or more people sign it, the White House staff will review it, ensure it’s sent to the appropriate policy experts, and issue an official response.
That's obviously not a commitment to do anything, but I don't think they can commit to anything. After all, we have three branches of government, and depending on the issue, one of those branches might have the most influence over any action or inaction. The president does own the bully pulpit though, and can certainly take ownership of things he can't directly influence.
Here are three petitions I have signed: