You are correct. Unfortunately, there are other factors in play.
Senator Orrin Hatch managed to attach his DREAM Act giving reduced tuition to illegals to a critical but unrelated bill, thus avoiding a floor vote.
Senator Craig's AGJOBS bill, which would result in eventual amnesty for up to 3 million illegals (and an effective pardon for their employers for all past transgressions) is headed the same way.
I received an email from NumbersUSA earlier today saying that the White House is pressuring the House of Representatives to remove language from the new 9/11 legislation that would make illegal immigration more difficult. At the time the email was sent, the House Republican leadership was standing firmly against the changes wanted by the White House.