Boehner's office says that attaching a rider abrogating the Executive Order items would accomplish nothing, since that section of the INS is self-funding and does not require re-authorization every year. The fallback is to hold back a portion of government revenues, which would just be a mini-shutdown: no H1Bs, no Green Cards, etc., for example. So Sen. Cruz had proposed a rider.
I haven't seen a response from Cruz on this point.
Is he conceding to Boehner that he was mistaken?
"(ii) CONGRESSIONAL ACTION.No major change may be implemented unless the Congress specifically provides, in an appropriations or other Act, for funds for implementation of the change.
Immigration Reform Control Act of 1986 "NOTICE TO CONGRESS BEFORE IMPLEMENTING CHANGES" (Required)