Is the Hunt Already Over?: A theory (H/T Kaus) that Reid was once an opponent of the bill but now wants to see the bill passed and has maneuvered to make it happen--quoting The Capitolist (an anonymous blog for Capitol Hill staffers):

immigration reform 2.0.: 22 ammendments, 11 dem, 11 rep. anyone who introduces an ammendment has pledged to vote for cloture. dorgan's ammendment is in. hutchison is on board. pay to play, legislative style.

If this is true, and, as the AP reports 16 of the 22 amendments of the new "package" have been proposed by (former) opponents of cloture, then we could have a switch of 16 votes right from that deal, including Boxer, Hutchison, Thune, Tester, Baucus, McCaskill, Grassley,** Coleman, Sanders, Webb, Bond, and Ensign. The Capitolist post says "dorgan's amendment is in"--does he have an amendment, too, what could it be? Who else?
If we add these 12 to some people very likely to switch--McConnell, Kyl, Lott, Craig--we're at 16 switchers: one more than needed.***
**This switching would be rather abrupt for Grassley, who was one of 6 senators who wrote a letter to President Bush saying that we needed more enforcement, but check out this thehill.com video of Grassley in which he says he'll vote against the bill if it has "amnesty" (see the last ten seconds or so)--he's not saying he'll vote against cloture.

***UPDATE: Though let's also remember that, since we don't (or at least I don't) know what the other amendments are, Kyl, McConnell, Lott, and Craig may also be proposing amendments--so their amendments could be included in the 16. Also, some of these 16 amendments may have multiple co-sponsors, so these 16 amendments could lead to more than 16 switches (e.g. Baucus and Tester are linked for one amendment). Or individual senators could be proposing multiple amendments--in which case these 16 amendments might not lead to 16 switches. Or we could have some combination....if this theory holds up at all...

UPDATE: Some sources are telling me that not every senator who has an amendment has agreed to vote for cloture. Is the amendments-for-cloture theory bogus? Partially right? But who's agreed to what? To anything?
Correction: Strike Cornyn: He doesn't have an amendment. (I don't think...)
UPDATE 2: I'm getting more skeptical about this theory (or think at least that it's not universal).