Sadly, Dick Cheney was the president of the Senate at the time, and presided over that sordid affair.
I believe that the Senate counts the Electoral College votes for the the Vice Presidential candidate. As President of the Senate VP Cheney is responsible for qualifying the winning VP candidate and certifying the VP candidates electoral college vote.
With that said, the Speaker of the House of Representatives is responsible for certifying the Electoral College votes of the presidential candidate. Nancy Pelosi was Speaker of the House at that time and was responsible for qualifying the winning presidential candidate and for certifying the Electoral College votes for the presidential candidates.
I believe that if Dick Cheney had any inkling that Obama could not legally be president and for some reason refused to speak up about it, then he shares some of the blame. However, in my opinion it is the Democrat Party and its state chapters and Nancy Pelosi in particular, who should share the blame and indeed be prosecuted for perpetrating this electoral fraud on America.
In addition, many state governments are also to blame for running the most corrupt election in American history. The media in America is also responsible for abetting the Democrats in this electoral fraud.
The President of the Senate (aka VP) does not run the senate.
The Senate is run by the Majority Leader who appoints a Pro-tem to run the day to day functioning of the body.
The VP is primarily a titular head and is directly involved only to break a tie vote since (particularly if his party is not in the majority) he cannot carry the votes for any issue.