Along with Corker, Lamar Alexander (R-TN) has just said "no" to cloture (H/T K-Lo):

“I will vote against cloture to end debate on the current immigration bill when it comes before us next week. Other than the war on terror, there is nothing more important than fixing our broken immigration system, and we must keep working on it for as long as it takes to get it right, but right must include a process that earns the confidence of the American people, and this bill does not do that.

This problem has been years in the making and will take time to fix. We must secure the border first once and for all, verified by credible sources, without amnesty – you are here legally or you are not here. We also must make it easier for highly skilled workers to come to America to create jobs and expect and assist those here legally to become Americans by speaking our language and appreciating our history and culture.

I will oppose any bill that does not include these essential elements.”