Cheney cannot vote on cloture, only in the case of a 50-50 tie. Since you need 60 votes for cloture, that won't happen.
Cheney's presence is indicated if there is a risk of successsful objection to cloture, that is, if cloture fails to pass. That is the procedural trigger for the "point of order" known as the nuclear option, or Constitutional option.
A point of order would be rasied by one Senator (probably Frist). The chair would rule on that point of order. Then the DEMs would call for an appeal of the ruling. That call for appeal is not debatable, but is voted on, with a simple majority having its way. That is where Cheny could break a tie.