This could play perfect in the Republican's hand, get a bill, any bill, on the floor at it's bare minimum and let the Rats block it. Amendments can always be added later, just concentrate on border security and enforcement.
The trouble is, Frist allowed the Specter/Kennedy/McCain version, with the amnesty and guest workers and instate tuition for illegal aliens and all the rest, come to floor. That's what they're debating, at the same time as the Frist border control version. Yes, as hideous as it sounds, they're both on the floor at the same time. Check out C-Span.