Frist is saying the immigration bill is posposed till tomorrow afternoon?
Frist docketed his personal immigration bill and a cloture motion (cloture on taking up the bill, not on passing the bill) last week Thursday. The object was to get the Judiciary Committee to get a move on. The Judiciary Committee did.
With regard to immigration, the first issue is which bill should be taken up? Frist's, which has a promise of Reid to filibuster, and which the cloture motion is aimed at cuting of debate on whether or not to take it up; or the Committee version, which Reid (probably) does not object to.
With regard to Senate action, Frist may want to finish the lobbying bill, or if not, permit some amount of debate as to which immigration bill should be debated.
I think Frist is grandstanding - flexing his muscles - by not outright making a substitution of the Committee Bill for his, and getting on with the debate. OTOH, he may face objection from his own party on getting unanimous consent to take up the Committee version. Instead of a DEM filibuster, he's facing a GOP filibuster.