I found reference to Federal Rules regarding counting of the Electoral Vote in an article from back in 2004 (when the Dems. objected). From that article it appears that the objection has to be filed by at least one member of the House, and one member of the Senate. My guess at this point is that there is not one Republican Senator in Washington that was even willing to broach this subject...
I’ll post a link if I find an official rules site.
3 USC 15 - Section 15
“Every objection shall be made in writing, and shall state clearly and concisely, and without argument, the ground thereof, and shall be signed by at least one Senator and one Member of the House of Representatives before the same shall be received.”
http://www4.law.cornell.edu/uscode/3/usc_sec_03_00000015——000-.html
If I’m reading this right, no one objected in writing beforehand, so Cheney didn’t have to call for it.