Will Domenici (R-NM) back cloture and the bill itself? Via the Politico's Immigration Map (which offers sound-bites on immigration from some senators):

Domenici has said that the bipartisan agreement reached on a comprehensive border security and immigration reform package represents the “best chance” to fix a broken U.S. system.

If he calls it the "best chance," then it sounds as though he's likely to vote for cloture and, probably, the bill itself. He voted for last year's immigration bill.