Osama tried to influence the 2004 election, and may even have succeeded. He released a video tape four days before the election, and several pundits asserted that this video helped Bush win. After the election, FOX News reported that John Kerry blamed the Osama tape for his loss.
OBL is many things to many people but all would agree that he is very intelligent and shrewd. His release of a tape four days before the 2004 election in which President Bush was attacked for his response to the 9/11 attacks was designed to achieve an emotional reaction in the American electorate. The timing was critical because little opportunity was given for any rational discussion of OBL's statements before the voting was conducted.
The fact that the tape criticized Bush was taken at first by some pundits to mean that OBL was promoting Kerry. On reflection, and after the election, the tape was seen to be pro-Bush. OBL must have known ahead of time that the American populace would react in a manner directly opposite to his stated intent. I believe that he knew this, and I believe that his intent was to get Bush reelected.
Why would he want Bush reelected? The argument can be made that OBL has been trying to provoke the United States since the first World Trade Center attack. If this was his intent, and he has so stated, then with the attacks of 9/11 he succeeded. President Bush responded to this provocation by invading Afghanistan and Iraq. OBL's strategy was to provoke the sleeping giant in the hope that his response would awaken and unite the Muslim world to OBL's vision of a new Caliphate.
Some have argued that Bush followed OBL's strategy as designed, to the Western World's universal detriment. The way this argument goes, the U.S. military actions in the Middle East have turned the Muslim world against us. More and more Muslims are rallying to OBL's banner. If we had not "overreacted" to the Al Qaeda attacks the World would still love us. The way to deal with the Al Qaeda terrorists is through law enforcement and the courts: arrest them, read them their rights and then put them on trial. If they go free, well, at least we have the self satisfaction that we protected their rights.
Not everyone agrees with this argument. My view is that we weren't that popular in the Muslim world before 9/11. The escalation of attacks by Al Qaeda was going to get worse if we continued to ignore them, not better. Assuming we were able to actually locate and arrest these terrorists, their trials would be security nightmares and propaganda bonanzas for OBL and his minions. The better solution is to take the fight to the enemy.
Would OBL rather face Hillary or Rudy as an opponent? A better question is whether he would rather face a Republican or a Democrat. His preference for a candidate will dictate his choice of actions. He has displayed a tendency for the dramatic. The most drama and the most impact would be some kind of action immediately prior to the election. He has already released a tape prior to the previous election, so the drama of this action would be lessened.
A better option for him would be a well planned, coordinated attack: his specialty. The attack would be immediately before the election. To execute such an attack the planning would even now be underway.