Won't happen for 2 main reasons IMHO
1) Cheney does not want to go and feels he is in the best place for his country and his President, all the time he feels that he will not resign. He has to resign he is elected. The President could ask him to go but not sack him and the President will not ask him to go because in IMHO he does not want him to go and also it would be seen as disloyalty and GWB value loyalty.
2) Cheney realises even if he wanted to go and IMHO he does not the fall out would be huge and would not only hurt the Bush administration but would hurt the re-election of the Republicans in the House and Senate. The RATS would jump on it saying it shows a divided party and leadership problems.
The third and perhaps the most damaging consideration is confirmation hearings even if the above 2 considerations are ignored.
Think of other recent ones including Rice's own for Secretary of State and John Bolton for UN Ambassador. Again too damaging for the administration and Party.
Also to be considered if Rice does not want to run for President that why would she accept/be pushed into a role which traditionally has been nothing position. Surely she is better off personally and more importantly where she is for her country.
Cheney's Vice Presidency is unique in the advice; some say power he wields; this would not be the same for Rice. For Rice it would be a demotion not promotion.
In conclusion, the President does not want it, Cheney does not want and Rice would not want it.
I agree with YOU snugs, and the Conservative Base doesn't want it either. We too, would look at it as a betrayal.