The Snowden petition had 146,511 signatures as of Wednesday afternoon, while the Bieber petition had 117,272.
Both petitions raise difficult issues for the Obama administration, which has mostly defended the spying programs revealed by Snowden and has been lobbying Congress for more open immigration policies.
The White House petition page says petitions will be removed if they:
•Threaten violence or harm to individuals or groups;
•Are obscene, vulgar or lewd;
•Contain defamatory or fraudulent statements;
•Contain profane, abusive or degrading terms or epithets;
•Contain information that invade a person’s privacy; or
•Contain information that would violate the law or give rise to civil liability.
There's no mention of declining to respond if a petition is potentially embarrassing politically, but the White House may decline to address certain aspects of the petition. The petition instructions also set no time limit for a response.
Seeing as that it has been seven months since the Snowden petition crossed the signature threshold, I wouldn’t hold my breath for a response on Bieber.
Update, 4:30 pm: A White House official said the Bieber petition would receive a response. That sounds nice, but the White House said in Novebmer 2013 that it would respond to the Snowden petition but has yet to do so.