It appears that you're missing something. Read the act's reference to subsection (c)(2) carefully. You see, there is no subsection (c)(2) in the proposed bill. It's a part of the law this would have amended, 18 USC § 2703.
And 18 USC § 2703(c)(2) requires no more than an administrative subpoena (though there are other ways to get it as well). And an administrative subpoena is not a warrant at all. But don't take my word for any of this, read it for yourself:
"(2) A provider of electronic communication service or remote computing service shall disclose to a governmental entity the [long list of customer info skipped] of a subscriber to or customer of such service when the governmental entity uses an administrative subpoena authorized by a Federal or State statute or a Federal or State grand jury or trial subpoena or any means available under paragraph (1)."
And 18 USC § 2703(c)(2) requires no more than an administrative subpoena (though there are other ways to get it as well). And an administrative subpoena is not a warrant at all. But don't take my word for any of this, read it for yourself:
"(2) A provider of electronic communication service or remote computing service shall disclose to a governmental entity the [long list of customer info skipped] of a subscriber to or customer of such service when the governmental entity uses an administrative subpoena authorized by a Federal or State statute or a Federal or State grand jury or trial subpoena or any means available under paragraph (1)."
Ref: http://www.law.cornell.edu/uscode/text/18/2703
It's like we have a software patch and everyone is reading only the patch, without considering what the existing code does.